Solve (9x+11)(x+9)=79

$$(9x+11)(x+9)=79$$

Solve for x

$$x=-10$$

$$x=-\frac{2}{9}\approx -0.222222222$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 9x+11 by x+9 and combine like terms.

$$9x^{2}+92x+99=79$$

Subtract 79 from both sides.

$$9x^{2}+92x+99-79=0$$

Subtract 79 from 99 to get 20.

$$9x^{2}+92x+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 9 for a, 92 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-92±\sqrt{92^{2}-4\times 9\times 20}}{2\times 9}$$

Square 92.

$$x=\frac{-92±\sqrt{8464-4\times 9\times 20}}{2\times 9}$$

Multiply -4 times 9.

$$x=\frac{-92±\sqrt{8464-36\times 20}}{2\times 9}$$

Multiply -36 times 20.

$$x=\frac{-92±\sqrt{8464-720}}{2\times 9}$$

Add 8464 to -720.

$$x=\frac{-92±\sqrt{7744}}{2\times 9}$$

Take the square root of 7744.

$$x=\frac{-92±88}{2\times 9}$$

Multiply 2 times 9.

$$x=\frac{-92±88}{18}$$

Now solve the equation x=\frac{-92±88}{18} when ± is plus. Add -92 to 88.

$$x=-\frac{4}{18}$$

Reduce the fraction \frac{-4}{18} to lowest terms by extracting and canceling out 2.

$$x=-\frac{2}{9}$$

Now solve the equation x=\frac{-92±88}{18} when ± is minus. Subtract 88 from -92.

$$x=-\frac{180}{18}$$

Divide -180 by 18.

$$x=-10$$

The equation is now solved.

$$x=-\frac{2}{9} x=-10$$

Steps for Completing the Square

Use the distributive property to multiply 9x+11 by x+9 and combine like terms.

$$9x^{2}+92x+99=79$$

Subtract 99 from both sides.

$$9x^{2}+92x=79-99$$

Subtract 99 from 79 to get -20.

$$9x^{2}+92x=-20$$

Divide both sides by 9.

$$\frac{9x^{2}+92x}{9}=-\frac{20}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$x^{2}+\frac{92}{9}x=-\frac{20}{9}$$

Divide \frac{92}{9}, the coefficient of the x term, by 2 to get \frac{46}{9}. Then add the square of \frac{46}{9} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+\frac{92}{9}x+\left(\frac{46}{9}\right)^{2}=-\frac{20}{9}+\left(\frac{46}{9}\right)^{2}$$

Square \frac{46}{9} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+\frac{92}{9}x+\frac{2116}{81}=-\frac{20}{9}+\frac{2116}{81}$$

Add -\frac{20}{9} to \frac{2116}{81} by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

$$x^{2}+\frac{92}{9}x+\frac{2116}{81}=\frac{1936}{81}$$

Factor x^{2}+\frac{92}{9}x+\frac{2116}{81}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{46}{9}\right)^{2}=\frac{1936}{81}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{46}{9}\right)^{2}}=\sqrt{\frac{1936}{81}}$$

Simplify.

$$x+\frac{46}{9}=\frac{44}{9} x+\frac{46}{9}=-\frac{44}{9}$$

Subtract \frac{46}{9} from both sides of the equation.

$$x=-\frac{2}{9} x=-10$$