Martin-Gay, Beginning Algebra, 5ed 22

Not all quadratic equations can be solved as in the previous examples. By using a method called completing the square, we can use the principle of square roots to solve any quadratic equation.

Solve x2 + 10x + 4 = 0

Martin-Gay, Beginning Algebra, 5ed 33

Martin-Gay, Beginning Algebra, 5ed 44

Isolate the variable terms.

Complete the square, by adding 25 to both sides.

Simplify.

Factor the perfect the square.

Square root property.

Solve for x.

Martin-Gay, Beginning Algebra, 5ed 55

EXAMPLE Solve x2 + 10x + 4 = 0 by completing the square.

2( 5) 21x

2 10 4 0x x

2 10 4x x

x2 + 10x + 25 = –4 + 25

5 21x

5 21x

Using the square root property.

Factoring the perfect square trinomial, and simplify.

Complete the square, by adding 25 to both sides.

Isolate the variable terms.

5 21 or 5 21x x

Solve for x.

Two solutions for x.

Plus Solution Minus Solution

Martin-Gay, Beginning Algebra, 5ed 66

EXAMPLE Solve 9t2 + 6t = 6 by completing the square.

Martin-Gay, Beginning Algebra, 5ed 77