SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

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solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

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Presentation transcript:

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

Completing the square If you expand the expressions (x + b)2 and (x – b)2 you should obtain the results: and Rearranging these gives you the following important results: This is known as completing the square.

1 Complete the square for the expression x2 − 8x. check:

2 Complete the square for the expression x2 + 6x. check:

3 Complete the square for the expression x2 − 12x. check:

4 Complete the square for the expression x2 + 5x. check:

5 Complete the square for the expression x2 + 4x + 12. check:

6 Complete the square for the expression x2 − 8x − 5. check:

You can solve quadratic equations by completing the square.

1 Solve the equation x2 − 8x − 5 = 0. add 5 to both sides complete the square add 16 to both sides square root add 4 to both sides

2 Solve the equation x2 + 10x − 7 = 0. add 7 to both sides complete the square add 25 to both sides square root take 5 from both sides