Solve 0=x^2+8x-58

$$0 = x ^ { 2 } + 8 x - 58$$

Solve for x (complex solution)

$$x=\sqrt{74}-4\approx 4.602325267$$

$$x=-\left(\sqrt{74}+4\right)\approx -12.602325267$$

Steps Using the Quadratic Formula

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

$$x^{2}+8x-58=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -58 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-58\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-58\right)}}{2}$$

Multiply -4 times -58.

$$x=\frac{-8±\sqrt{64+232}}{2}$$

Add 64 to 232.

$$x=\frac{-8±\sqrt{296}}{2}$$

Take the square root of 296.

$$x=\frac{-8±2\sqrt{74}}{2}$$

Now solve the equation x=\frac{-8±2\sqrt{74}}{2} when ± is plus. Add -8 to 2\sqrt{74}.

$$x=\frac{2\sqrt{74}-8}{2}$$

Divide -8+2\sqrt{74} by 2.

$$x=\sqrt{74}-4$$

Now solve the equation x=\frac{-8±2\sqrt{74}}{2} when ± is minus. Subtract 2\sqrt{74} from -8.

$$x=\frac{-2\sqrt{74}-8}{2}$$

Divide -8-2\sqrt{74} by 2.

$$x=-\sqrt{74}-4$$

The equation is now solved.

$$x=\sqrt{74}-4 x=-\sqrt{74}-4$$

Steps for Completing the Square

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

$$x^{2}+8x-58=0$$

Add 58 to both sides. Anything plus zero gives itself.

$$x^{2}+8x=58$$

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.

$$x^{2}+8x+4^{2}=58+4^{2}$$

Square 4.

$$x^{2}+8x+16=58+16$$

Add 58 to 16.

$$x^{2}+8x+16=74$$

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}.

$$\left(x+4\right)^{2}=74$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{74}$$

Simplify.

$$x+4=\sqrt{74} x+4=-\sqrt{74}$$

Subtract 4 from both sides of the equation.

$$x=\sqrt{74}-4 x=-\sqrt{74}-4$$

Solve for x

$$x=\sqrt{74}-4\approx 4.602325267$$

$$x=-\sqrt{74}-4\approx -12.602325267$$

Steps Using the Quadratic Formula

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

$$x^{2}+8x-58=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 8 for b, and -58 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-8±\sqrt{8^{2}-4\left(-58\right)}}{2}$$

Square 8.

$$x=\frac{-8±\sqrt{64-4\left(-58\right)}}{2}$$

Multiply -4 times -58.

$$x=\frac{-8±\sqrt{64+232}}{2}$$

Add 64 to 232.

$$x=\frac{-8±\sqrt{296}}{2}$$

Take the square root of 296.

$$x=\frac{-8±2\sqrt{74}}{2}$$

Now solve the equation x=\frac{-8±2\sqrt{74}}{2} when ± is plus. Add -8 to 2\sqrt{74}.

$$x=\frac{2\sqrt{74}-8}{2}$$

Divide -8+2\sqrt{74} by 2.

$$x=\sqrt{74}-4$$

Now solve the equation x=\frac{-8±2\sqrt{74}}{2} when ± is minus. Subtract 2\sqrt{74} from -8.

$$x=\frac{-2\sqrt{74}-8}{2}$$

Divide -8-2\sqrt{74} by 2.

$$x=-\sqrt{74}-4$$

The equation is now solved.

$$x=\sqrt{74}-4 x=-\sqrt{74}-4$$

Steps for Completing the Square

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

$$x^{2}+8x-58=0$$

Add 58 to both sides. Anything plus zero gives itself.

$$x^{2}+8x=58$$

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.

$$x^{2}+8x+4^{2}=58+4^{2}$$

Square 4.

$$x^{2}+8x+16=58+16$$

Add 58 to 16.

$$x^{2}+8x+16=74$$

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}.

$$\left(x+4\right)^{2}=74$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+4\right)^{2}}=\sqrt{74}$$

Simplify.

$$x+4=\sqrt{74} x+4=-\sqrt{74}$$

Subtract 4 from both sides of the equation.

$$x=\sqrt{74}-4 x=-\sqrt{74}-4$$