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# Complete the square

With quadratic expression like x2 + bx, you can complete the square by adding $(\frac{b}{2})^2$

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

x2 + 8x +

Add $(\frac{b}{2})^2$ to complete the square.

x2 + 8x + $(\frac{b}{2})^2$

 = x2 + 8x + $(\frac{b}{2})^2$ Plug in b=8 = x2 + 8x + $(\frac{8}{2})^2$ Divide = x2 + 8x + 42 Square = x2 + 8x + 16

This quadratic can be written as a square, (x + 4)2, so it is a perfect-square quadratic.

The number needed to complete the square was 16.

Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.

z2-12z +