Solve 0=x^2+8x-576

$$0 = x ^ { 2 } + 8 x - 576$$

Solve for x

$$x=4\sqrt{37}-4\approx 20.331050121$$

$$x=-4\sqrt{37}-4\approx -28.331050121$$

Steps Using the Quadratic Formula

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

$$x^{2}+8x-576=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -576 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-576\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-576\right)}}{2}$$

Multiply -4 times -576.

$$x=\frac{-8±\sqrt{64+2304}}{2}$$

Add 64 to 2304.

$$x=\frac{-8±\sqrt{2368}}{2}$$

Take the square root of 2368.

$$x=\frac{-8±8\sqrt{37}}{2}$$

Now solve the equation x=\frac{-8±8\sqrt{37}}{2} when ± is plus. Add -8 to 8\sqrt{37}.

$$x=\frac{8\sqrt{37}-8}{2}$$

Divide -8+8\sqrt{37} by 2.

$$x=4\sqrt{37}-4$$

Now solve the equation x=\frac{-8±8\sqrt{37}}{2} when ± is minus. Subtract 8\sqrt{37} from -8.

$$x=\frac{-8\sqrt{37}-8}{2}$$

Divide -8-8\sqrt{37} by 2.

$$x=-4\sqrt{37}-4$$

The equation is now solved.

$$x=4\sqrt{37}-4 x=-4\sqrt{37}-4$$

Steps for Completing the Square

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

$$x^{2}+8x-576=0$$

Add 576 to both sides. Anything plus zero gives itself.

$$x^{2}+8x=576$$

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.

$$x^{2}+8x+4^{2}=576+4^{2}$$

Square 4.

$$x^{2}+8x+16=576+16$$

Add 576 to 16.

$$x^{2}+8x+16=592$$

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}.

$$\left(x+4\right)^{2}=592$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{592}$$

Simplify.

$$x+4=4\sqrt{37} x+4=-4\sqrt{37}$$

Subtract 4 from both sides of the equation.

$$x=4\sqrt{37}-4 x=-4\sqrt{37}-4$$