Solve (x+2)(x+6)=2x+4

$$(x+2)(x+6)=2x+4$$

Solve for x

$$x=-4$$

$$x=-2$$

Steps Using the Quadratic Formula

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

$$x^{2}+8x+12=2x+4$$

Subtract 2x from both sides.

$$x^{2}+8x+12-2x=4$$

Combine 8x and -2x to get 6x.

$$x^{2}+6x+12=4$$

Subtract 4 from both sides.

$$x^{2}+6x+12-4=0$$

Subtract 4 from 12 to get 8.

$$x^{2}+6x+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 6 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-6±\sqrt{6^{2}-4\times 8}}{2}$$

Square 6.

$$x=\frac{-6±\sqrt{36-4\times 8}}{2}$$

Multiply -4 times 8.

$$x=\frac{-6±\sqrt{36-32}}{2}$$

Add 36 to -32.

$$x=\frac{-6±\sqrt{4}}{2}$$

Take the square root of 4.

$$x=\frac{-6±2}{2}$$

Now solve the equation x=\frac{-6±2}{2} when ± is plus. Add -6 to 2.

$$x=-\frac{4}{2}$$

Divide -4 by 2.

$$x=-2$$

Now solve the equation x=\frac{-6±2}{2} when ± is minus. Subtract 2 from -6.

$$x=-\frac{8}{2}$$

Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=-2 x=-4$$

Steps for Completing the Square

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

$$x^{2}+8x+12=2x+4$$

Subtract 2x from both sides.

$$x^{2}+8x+12-2x=4$$

Combine 8x and -2x to get 6x.

$$x^{2}+6x+12=4$$

Subtract 12 from both sides.

$$x^{2}+6x=4-12$$

Subtract 12 from 4 to get -8.

$$x^{2}+6x=-8$$

Divide 6, the coefficient of the x term, by 2 to get 3. Then add the square of 3 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+6x+3^{2}=-8+3^{2}$$

Square 3.

$$x^{2}+6x+9=-8+9$$

Add -8 to 9.

$$x^{2}+6x+9=1$$

Factor x^{2}+6x+9. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+3\right)^{2}=1$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+3\right)^{2}}=\sqrt{1}$$

Simplify.

$$x+3=1 x+3=-1$$

Subtract 3 from both sides of the equation.

$$x=-2 x=-4$$