Solve (x-2)(x+6)=3^2

$$( x - 2 ) ( x + 6 ) = 3 ^ { 2 }$$

Solve for x

$$x=-7$$

$$x=3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-2 by x+6 and combine like terms.

$$x^{2}+4x-12=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+4x-12=9$$

Subtract 9 from both sides.

$$x^{2}+4x-12-9=0$$

Subtract 9 from -12 to get -21.

$$x^{2}+4x-21=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 4 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-4±\sqrt{4^{2}-4\left(-21\right)}}{2}$$

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-21\right)}}{2}$$

Multiply -4 times -21.

$$x=\frac{-4±\sqrt{16+84}}{2}$$

Add 16 to 84.

$$x=\frac{-4±\sqrt{100}}{2}$$

Take the square root of 100.

$$x=\frac{-4±10}{2}$$

Now solve the equation x=\frac{-4±10}{2} when ± is plus. Add -4 to 10.

$$x=\frac{6}{2}$$

Divide 6 by 2.

$$x=3$$

Now solve the equation x=\frac{-4±10}{2} when ± is minus. Subtract 10 from -4.

$$x=-\frac{14}{2}$$

Divide -14 by 2.

$$x=-7$$

The equation is now solved.

$$x=3 x=-7$$

Steps for Completing the Square

Use the distributive property to multiply x-2 by x+6 and combine like terms.

$$x^{2}+4x-12=3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$x^{2}+4x-12=9$$

Add 12 to both sides.

$$x^{2}+4x=9+12$$

Add 9 and 12 to get 21.

$$x^{2}+4x=21$$

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+4x+2^{2}=21+2^{2}$$

Square 2.

$$x^{2}+4x+4=21+4$$

Add 21 to 4.

$$x^{2}+4x+4=25$$

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=25$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{25}$$

Simplify.

$$x+2=5 x+2=-5$$

Subtract 2 from both sides of the equation.

$$x=3 x=-7$$