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Wednesday 27th of September
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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Completing the Square

Procedure â€” To Complete the Square

To complete the square for a binomial of the form x2 + bx:

Step 1 Calculate Â· b.

(That is, divide b by 2.)

Step 2 Square the result from Step 1.

That is, calculate .

Step 3 Add the result from Step 2 to x2 + bx.

The new expression, x2 + bx + , is a perfect square trinomial.

Example

Complete the square for each binomial. Then write each new expression as the square of a binomial.

a. x2 + 12x

b. x2 - 5x

Solution

 a. x2 + 12x has the form x2 + bx, where b = 12. Step 1 Calculate Step 2 Square the result from Step 1. Step 3 Add the result from Step 2 to x2 + bx. 62 = 36 x2 + 12x + 36 b. Write the expression x2 + 12x + 36 as the square of a binomial.x2 - 5x has the form x2 + bx, where b = -5. = (x + 6)2 Step 1 Calculate Step 2 Square the result from Step 1. Step 3 Add the result from Step 2 to x2 + bx.

We have completed the square.

Write the expression as the square of a binomial.

Notes:

The expression x2 + 12x + 36 is a perfect square trinomial.

The expression is a perfect square trinomial.