Homework: Part I

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Homework Part I
Solve using square roots. Check your answers. 1.
x2 195 1 2. 4x2 18 9 3. 2x2 10 12
4. Solve 0 5x2 225. Round to the nearest
hundredth.
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Homework Part II
5. A community swimming pool is in the shape of a
trapezoid. The height of the trapezoid is twice
as long as the shorter base and the longer base
is twice as long as the height.
The area of the pool is 3675 square feet. What is
the length of the longer base? Round to the
nearest foot.
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Warm Up Find each square root. Solve each
equation. 5. 6x 60 6. 7. 2x 40 0 8.
5x 3
6
11
1.
2.
4.
25
3.
x 80
x 10
x 20
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Additional Example 1A Using Square Roots to
Solve x2 a
Solve using square roots. Check your answer.
x2 169
Solve for x by taking the square root of both
sides. Use to show both square roots.
x 13
The solutions are 13 and 13.
Substitute 13 into the original equation.
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Additional Example 1A Continued
Solve using square roots. Check your answer.
Check
Substitute 13 into the original equation.
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Additional Example 1B Using Square Roots to
Solve x2 a
Solve using square roots.
x2 49
There is no real number whose square is negative.
There is no real solution. The solution set is
the empty set, ø.
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Partner Share! Example 1a
Solve using square roots. Check your answer.
x2 121
Solve for x by taking the square root of both
sides. Use to show both square roots.
x 11
The solutions are 11 and 11.
Substitute 11 into the original equation.
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Check It Out! Example 1a Continued
Solve using square roots. Check your answer.
Check
Substitute 11 into the original equation.
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Partner Share! Example 1b
Solve using square roots. Check your answer.
x2 0
Solve for x by taking the square root of both
sides. Use to show both square roots.
x 0
The solution is 0.
Substitute 0 into the original equation.
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Partner Share! Example 1c
Solve using square roots. Check your answer.
x2 16
There is no real number whose square is negative.
There is no real solution. The solution set is
the empty set, ø.
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If a quadratic equation is not written in the
form x2 a, use inverse operations to isolate x2
before taking the square root of both sides.
(Remember, a must be positive.)
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Additional Example 2A Using Square Roots to
Solve Quadratic Equations
Solve using square roots.
x2 7 7
Subtract 7 from both sides.
Take the square root of both sides.
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Additional Example 2B Using Square Roots to
Solve Quadratic Equations
Solve using square roots.
16x2 49 0
16x2 49 0
49 49
Add 49 to both sides.
Divide by 16 on both sides.
Take the square root of both sides. Use to show
both square roots.
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Additional Example 2B Continued
Solve using square roots.
Check 16x2 49 0
16x2 49 0
?
?
0 0
0 0
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Partner Share! Example 2a
Solve by using square roots. Check your answer.
100x2 49 0
Subtract 49 from both sides.
Divide by 100 on both sides.
There is no real number whose square is negative.
ø
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Check It Out! Example 2b
Solve by using square roots. Check your answer.
36x2 1
Divide by 36 on both sides.
Take the square root of both sides. Use to show
both square roots.
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Check It Out! Example 2b Continued
Solve by using square roots. Check your answer.
Check 36x2 1
36x2 1
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When solving quadratic equations by using square
roots, the solutions may be irrational. In this
case, you can give the exact solutions by leaving
the square root in your answer, or you can
approximate the solutions by rounding to the
hundredths place.
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Additional Example 3A Approximating Solutions
Solve. Round to the nearest hundredth.
x2 15
Take the square root of both sides.
x ? ?3.87
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Additional Example 3B Approximating Solutions
Solve. Round to the nearest hundredth.
3x2 90 0
Subtract 90 from both sides.
Divide by 3 on both sides.
x2 30
Take the square root of both sides.
x ? ?5.48
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Additional Example 3B Continued
Solve. Round to the nearest hundredth.
3x2 90 0
Check Use a graphing calculator to support your
answer.
Use the zero function. The approximate solutions
are 5.48 and 5.48.
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Partner Share! Example 3a
Solve. Round to the nearest hundredth.
0 90 x2
Add x2 to both sides.
Take the square root of both sides.
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Check It Out! Example 3a Continued
Solve. Round to the nearest hundredth.
0 90 x2
Check Use a graphing calculator to support your
answer.
Use the zero function. The approximate solutions
are 9.49 and 9.49.
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Check It Out! Example 3b
Solve. Round to the nearest hundredth.
2x2 64 0
Add 64 to both sides.
Divide by 2 on both sides.
x2 32
Take the square root of both sides.
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Check It Out! Example 3b Continued
Solve. Round to the nearest hundredth.
2x2 64 0
Check Use a graphing calculator to support your
answer.
Use the zero function. The approximate solutions
are 5.66 and 5.66.
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Partner Share! Example 3c
Solve. Round to the nearest hundredth.
x2 45 0
x2 45 0
Subtract 45 from both sides.
There is no real number whose square is negative.
ø
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Additional Example 4 Application
Ms. Pirzada is building a retaining wall along
one of the long sides of her rectangular garden.
The garden is twice as long as it is wide. It
also has an area of 578 square feet. What will be
the length of the retaining wall?
Let x represent the width of the garden.
lw A
Use the formula for area of a rectangle.
l 2w
Length is twice the width.
Substitute x for w, 2x for l, and 578 for A.
2x2 578
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Additional Example 4 Continued
2x2 578
Divide both sides by 2.
Take the square root of both sides.
x 17
Negative numbers are not reasonable for width, so
x 17 is the only solution that makes sense.
Therefore, the length is 2w or 34 feet.
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Partner Share! Example 4
A lot is shaped like a trapezoid with bases x and
2x. Its area is 6000 ft2. Find x. Round to the
nearest foot.
(Hint Use )
Use the formula for area of a trapezoid.
Substitute 2x for h and b1, x for b2 , and 6000
for A.
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Partner Share! Example 4 Continued
Divide by 3 on both sides.
Take the square root of both sides.
Negative numbers are not reasonable for width, so
x 45 is the only solution that makes sense.
Therefore, x is approximately 45 feet.
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Lesson Review Part I
Solve using square roots. Check your answers. 1.
x2 195 1 2. 4x2 18 9 3. 2x2 10 12
4. Solve 0 5x2 225. Round to the nearest
hundredth.
14
ø
6.71
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Lesson Review Part II
5. A community swimming pool is in the shape of a
trapezoid. The height of the trapezoid is twice
as long as the shorter base and the longer base
is twice as long as the height.
The area of the pool is 3675 square feet. What is
the length of the longer base? Round to the
nearest foot.
108 feet