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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solve Quadratic Equations by Completing the Square

Goals • Solve quadratic equations by completing
the square.

VOCABULARY
Completing the square Adding a constant c to an
expression of the form x2 + bx to form a perfect
square trinomial

COMPLETING THE SQUARE

Words
To complete the square for the expression
x2 + bx, add the square of half the coefficient
of x.

Algebra

Example 1 Complete the square

Find the value of c that makes the expression
x2 - 5x + c a perfect square trinomial. Then write
the expression as the square of the binomial.

Solution
Step 1
Find the value of c.

Find the square of half the
coefficient of x.

Step 2 Write the expression as a perfect square trinomial.
Then write the expression as the square of a
binomial.

Substitute for c.

Square of a binomial

● Guided Practice Find the value of c that makes the
expression a perfect square trinomial. Then write
the expression as the square of a binomial.

Example 2 Multiple Choice Practice

What quantity should be added to both sides of this
equation to complete the square?

x2 - 16x = 10

A -64
B -8
C 8
D 64

Solution
Find the square of half of the coefficient of x:

The correct answer is D . A B C D

Example 3 Solve a quadratic equation

Solve 4x2 - 16x + 8 = 0 by completing the square.

Solution

 Write original equation. Subtract 8 from each side. Be sure that the coefficient of x2 is 1 before you complete the square. Divide each side by 4 . Add or , to each side. Write left side as the square of a binomial. Take square roots of each side. Add 2 to each side. The solutions are

Check To check the solutions
of 4x2  16x + 8 = 0, graph
the related function.

The x-intercepts are
approximately 0.6 and 3.4.
Compare these values with
the solutions:

Homework