Page 58 - Math Course 3 (Book 1)

Solving Quadratic Equations

x = 9 ± 8 Simplify. Use a calculator to evaluate each value of x.
x = 9 + 8 or x = 9 – 8 Separate the solutions. x = 40 + 1100 x = 40 – 1100

= 17 = 1 Simplify. ≈ 73.166 ≈ 6.834
Examine
Answer The solution set is {1, 17}. The solutions of the equation are about 7 ft and
about 73 ft. The solutions are distances from one
shore. Since the river is about 80 ft wide,
80 – 73 = 7.
Solve a Quadratic Equation in Which a ≠ 1
Answer He must stay within about 7 feet
of either bank.
Example

CANOEING Your Turn!
Suppose the rate of flow of an 80-foot-wide river is
2
given by the equation r = –0.01x + 0.8x where r is
the rate in miles per hour, and x is the distance from Solve an Equation by Completing the Square
the shore in feet. Joacquim does not want to pad- Solve x – 8x + 10 = 30.
2
dle his canoe against a current faster than 5 miles
per hour. At what distance from the river bank must
he paddle in order to avoid a current of 5 miles per A. {–2, 10}
hour? B. {2, –10}
C. {2, 10}
Explore D. Ø
You know the function that relates distance from
shore to the rate of the river current. You want to
know how far away from the river bank he must Answer
paddle to avoid the current.

Plan
Find the distance when r = 5. Use completing the
square to solve –0.01x² + 0.8x = 5. Solve a Quadratic Equation in Which a ≠ 1
Solve CANOEING

Suppose the rate of flow of a 60-foot-wide river is
–0.01x² + 0.8x = 5 Equation for the current. given by the equation r = –0.01x + 0.6x where r is
2
the rate in miles per hour, and x is the distance from
–0.001x² + 0.8x 5 Divide each side by the shore in feet. Joacquim does not want to paddle
–0.01 = –0.01 –0.01.
his canoe against a current faster than 5 miles per
x² – 80x = –500 Simplify. hour. At what distance from the river bank must
he paddle in order to avoid a current of 5 miles per
x2 – 80x + 1600 = –500 + 1600 Since = 1600 hour?

add 1600 to each side. A. 6 feet
B. 5 feet
2
(x – 40)² = 1100 Factor x – 80x + 1600. C. 1 foot
D. 10 feet
x – 40 = ± 1100 Take the square root of
each side.

1100
x = ± + 40 Add 40 to each side.
Answer
x = 40 ± 1100 Simplify.

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