Solve 0=x^2+11x-8

$$0 = x ^ { 2 } + 11 x - 8$$

Solve for x

$$x=\frac{3\sqrt{17}-11}{2}\approx 0.684658438$$

$$x=\frac{-3\sqrt{17}-11}{2}\approx -11.684658438$$

Steps Using the Quadratic Formula

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

$$x^{2}+11x-8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 11 for b, and -8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-11±\sqrt{11^{2}-4\left(-8\right)}}{2}$$

Square 11.

$$x=\frac{-11±\sqrt{121-4\left(-8\right)}}{2}$$

Multiply -4 times -8.

$$x=\frac{-11±\sqrt{121+32}}{2}$$

Add 121 to 32.

$$x=\frac{-11±\sqrt{153}}{2}$$

Take the square root of 153.

$$x=\frac{-11±3\sqrt{17}}{2}$$

Now solve the equation x=\frac{-11±3\sqrt{17}}{2} when ± is plus. Add -11 to 3\sqrt{17}.

$$x=\frac{3\sqrt{17}-11}{2}$$

Now solve the equation x=\frac{-11±3\sqrt{17}}{2} when ± is minus. Subtract 3\sqrt{17} from -11.

$$x=\frac{-3\sqrt{17}-11}{2}$$

The equation is now solved.

$$x=\frac{3\sqrt{17}-11}{2} x=\frac{-3\sqrt{17}-11}{2}$$

Steps for Completing the Square

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

$$x^{2}+11x-8=0$$

Add 8 to both sides. Anything plus zero gives itself.

$$x^{2}+11x=8$$

Divide 11, the coefficient of the x term, by 2 to get \frac{11}{2}. Then add the square of \frac{11}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+11x+\left(\frac{11}{2}\right)^{2}=8+\left(\frac{11}{2}\right)^{2}$$

Square \frac{11}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}+11x+\frac{121}{4}=8+\frac{121}{4}$$

Add 8 to \frac{121}{4}.

$$x^{2}+11x+\frac{121}{4}=\frac{153}{4}$$

Factor x^{2}+11x+\frac{121}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+\frac{11}{2}\right)^{2}=\frac{153}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+\frac{11}{2}\right)^{2}}=\sqrt{\frac{153}{4}}$$

Simplify.

$$x+\frac{11}{2}=\frac{3\sqrt{17}}{2} x+\frac{11}{2}=-\frac{3\sqrt{17}}{2}$$

Subtract \frac{11}{2} from both sides of the equation.

$$x=\frac{3\sqrt{17}-11}{2} x=\frac{-3\sqrt{17}-11}{2}$$