2. 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 x 2 + 10x + 4 = 0

3. Martin-Gay, Beginning Algebra, 5ed 33

4. 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.

5. Martin-Gay, Beginning Algebra, 5ed 55 EXAMPLESolve x 2 + 10x + 4 = 0 by completing the square. x 2 + 10x + 25 = –4 + 25 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. Solve for x. Two solutions for x. Plus SolutionMinus Solution

6. Martin-Gay, Beginning Algebra, 5ed 66 EXAMPLESolve 9t 2 + 6t = 6 by completing the square.

7. Martin-Gay, Beginning Algebra, 5ed 77