Solve (x-2)(x+4)=7

$$( x - 2 ) ( x + 4 ) = 7$$

Solve for x

$$x=-5$$

$$x=3$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-2 by x+4 and combine like terms.

$$x^{2}+2x-8=7$$

Subtract 7 from both sides.

$$x^{2}+2x-8-7=0$$

Subtract 7 from -8 to get -15.

$$x^{2}+2x-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-15\right)}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{-2±\sqrt{4+60}}{2}$$

Add 4 to 60.

$$x=\frac{-2±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{-2±8}{2}$$

Now solve the equation x=\frac{-2±8}{2} when ± is plus. Add -2 to 8.

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

Divide 6 by 2.

$$x=3$$

Now solve the equation x=\frac{-2±8}{2} when ± is minus. Subtract 8 from -2.

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

Divide -10 by 2.

$$x=-5$$

The equation is now solved.

$$x=3 x=-5$$

Steps for Completing the Square

Use the distributive property to multiply x-2 by x+4 and combine like terms.

$$x^{2}+2x-8=7$$

Add 8 to both sides.

$$x^{2}+2x=7+8$$

Add 7 and 8 to get 15.

$$x^{2}+2x=15$$

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=15+1^{2}$$

Square 1.

$$x^{2}+2x+1=15+1$$

Add 15 to 1.

$$x^{2}+2x+1=16$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=16$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{16}$$

Simplify.

$$x+1=4 x+1=-4$$

Subtract 1 from both sides of the equation.

$$x=3 x=-5$$