Question

Rewrite the function by completing the square.f(x) = x² + 12x - 69​

Answer 1

Answer:

x=−6−√105 or x=−6+√105

Step-by-step explanation:

Set the function equal to 0

0=x²+12x−69        Subtract x² from both sides.

0−x²=x²+12x−69−x²

−x²=12x−69      Subtract 12x from both sides.

−x²−12x=12x−69−12x

−x²−12x=−69        Divide both sides by -1.

$\frac{-x^{2}-2x }{-1} = \frac{-69}{-1}$

x²+12x=69       Add (12/2)^2=36 to both sides to complete the square.

x²+12x+36=69+36

x²+12x+36=105       Factor left side.

(x+6)²=105          Take square root of both sides

x+6=±√105         Add -6 to both sides.

x+6+−6=−6±√105

x=−6±√105       Write out both solutions

x=−6−√105 or x=−6+√105

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