Problem

Solve each equation by completing the square. See Example 1 and 2.EXAMPLE using Completing...

Solve each equation by completing the square. See Example 1 and 2.

EXAMPLE using Completing the Square (a = 1)

Solve x2 − 4x − 14 = 0.

Solution x2 − 4x − 14 = 0

Step 1 This step is not necessary since a = 1.

EXAMPLE using Completing the Square ( a ≠ 1 )

Solve 9x2 − 12x + 9 = 0.

The Quadratic Formula If we start with the equation, ax2 + bx + c = 0, for a > 0, and complete the square to solve for x in terms of the constants a, b, and c, the result is a general formula for solving any quadratic equation.

Square half the coefficient of x:

Quadratic Formula

The solutions of the quadratic equation ax2 + bx + c = 0, where a ≠ 0, are given by the quadratic formula.

x2 − 10x + 18 = 0

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Solutions For Problems in Chapter 1.4

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