Solve {l}{x(x+9)=9(x+4)}{text{solutionsetis}{6,-6|}}

$$\left. \begin{array} { l } { x ( x + 9 ) = 9 ( x + 4 ) } \\ { \text { solution set is } \{ 6 , - 6 | \} } \end{array} \right.$$

Solve for x

$$x=-6$$

$$x=6$$

Steps by Finding Square Root

Use the distributive property to multiply x by x+9.

$$x^{2}+9x=9\left(x+4\right)$$

Use the distributive property to multiply 9 by x+4.

$$x^{2}+9x=9x+36$$

Subtract 9x from both sides.

$$x^{2}+9x-9x=36$$

Combine 9x and -9x to get 0.

$$x^{2}=36$$

Take the square root of both sides of the equation.

$$x=6 x=-6$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+9.

$$x^{2}+9x=9\left(x+4\right)$$

Use the distributive property to multiply 9 by x+4.

$$x^{2}+9x=9x+36$$

Subtract 9x from both sides.

$$x^{2}+9x-9x=36$$

Combine 9x and -9x to get 0.

$$x^{2}=36$$

Subtract 36 from both sides.

$$x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-36\right)}}{2}$$

Multiply -4 times -36.

$$x=\frac{0±\sqrt{144}}{2}$$

Take the square root of 144.

$$x=\frac{0±12}{2}$$

Now solve the equation x=\frac{0±12}{2} when ± is plus. Divide 12 by 2.

$$x=6$$

Now solve the equation x=\frac{0±12}{2} when ± is minus. Divide -12 by 2.

$$x=-6$$

The equation is now solved.

$$x=6 x=-6$$