Solve 308=x*(x+8)

$$308=x \times (x+8)$$

Solve for x

$$x=-22$$

$$x=14$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x by x+8.

$$308=x^{2}+8x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+8x=308$$

Subtract 308 from both sides.

$$x^{2}+8x-308=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -308 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-308\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-308\right)}}{2}$$

Multiply -4 times -308.

$$x=\frac{-8±\sqrt{64+1232}}{2}$$

Add 64 to 1232.

$$x=\frac{-8±\sqrt{1296}}{2}$$

Take the square root of 1296.

$$x=\frac{-8±36}{2}$$

Now solve the equation x=\frac{-8±36}{2} when ± is plus. Add -8 to 36.

$$x=\frac{28}{2}$$

Divide 28 by 2.

$$x=14$$

Now solve the equation x=\frac{-8±36}{2} when ± is minus. Subtract 36 from -8.

$$x=-\frac{44}{2}$$

Divide -44 by 2.

$$x=-22$$

The equation is now solved.

$$x=14 x=-22$$

Steps for Completing the Square

Use the distributive property to multiply x by x+8.

$$308=x^{2}+8x$$

Swap sides so that all variable terms are on the left hand side.

$$x^{2}+8x=308$$

Divide 8, the coefficient of the x term, by 2 to get 4. Then add the square of 4 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+8x+4^{2}=308+4^{2}$$

Square 4.

$$x^{2}+8x+16=308+16$$

Add 308 to 16.

$$x^{2}+8x+16=324$$

Factor x^{2}+8x+16. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+4\right)^{2}=324$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{324}$$

Simplify.

$$x+4=18 x+4=-18$$

Subtract 4 from both sides of the equation.

$$x=14 x=-22$$