Quadratic Equations and Perfect Square trinomial, questions help

OPEN ENDED: Write a perfect square trinomial equation in which the linear coefficient is

negative and the constant term is a fraction. Then solve the equation.

Writing in Math: Use the information on page 288 to explain how you can find the time it takes

an accelerating car to reach the finish line. Include an explanation of why t2 + 22t + 121 = 246

cannot be solved by factoring and a description of the steps you would take to solve the

equation.

5-5
Completing the Square
Main Ideas
. Solve quadratic
equations by using
the Square Root
Property
. Solve quadratic
equations by
completing the
square
GET READY for the Lesson
Under a yellow caution flag, race car
drivers slow to a speed of 60 miles per
hour. When the green flag is waved,
the drivers can increase their speed.
Suppose the driver of one car is 500
feet from the finish line. If the driver
accelerates at a constant rate of 8 feet
per second squared, the equation
12 +22+ + 121 = 246 represents the
time t it takes the driver to reach this
line. To solve this equation, you can use
the Square Root Property.
New Vocabulary
completing the square
Square Root Property You have solved equations like x2 – 25 = 0 by
factoring. You can also use the Square Root Property to solve such an
equation. This method is useful with equations like the one above that
describes the race car’s speed. In this case, the quadratic equation
contains a perfect square trinomial set equal to a constant.
EXAMPLE Equation with Rational Roots
Solve x? + 10x + 25 = 49 by using the Square Root Property.
x? + 10x + 25 = 49 Original equation
(x + 5)2 = 49 Factor the perfect square trinomial.
x+5=149 Square Root Property
*+5 = +7
V 497
x= -5 +7 Add-5 to each side.
x=-5+7 or r=-5-7 Write as two equations.
= 2
I= -12 Solve each equation
The solution set is (2, -12). You can check this result by using factoring
to solve the original equation.
CHECK Your Progress
Solve each equation by using the Square Root Property.
1A. x2 – 12x + 36 = 25 1B. x2 – 16x + 64 = 49
Roots that are irrational numbers may be written as exact answers in radical
form or as approximate answers in decimal form when a calculator is used.
268 Chapter 5 Quadratic Functions and Inequalities