Solve Quadratic Equations by Completing the Square
Goals • Solve quadratic equations by completing
Completing the square Adding a constant c to an
expression of the form x2 + bx to form a perfect
COMPLETING THE SQUARE
To complete the square for the expression
x2 + bx, add the square of half the coefficient
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.
Step 1 Find the value of c.
Find the square of half the
coefficient of x.
Step 2 Write the expression as a perfect
Then write the expression as the square of a
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
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.
from each side.
|Be sure that the
coefficient of x2
is 1 before you
||Divide each side
by 4 .
||or , to
||Write left side as
the square of a
||Take square roots
of each side.
||Add 2 to
||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