Solve 11x^2-56+104=0

$$11 { x }^{ 2 } -56+104=0$$

Solve for x (complex solution)

$$x=-\frac{4\sqrt{33}i}{11}\approx -0-2.088931871i$$

$$x=\frac{4\sqrt{33}i}{11}\approx 2.088931871i$$

Steps by Finding Square Root

Add -56 and 104 to get 48.

$$11x^{2}+48=0$$

Subtract 48 from both sides. Anything subtracted from zero gives its negation.

$$11x^{2}=-48$$

Divide both sides by 11.

$$x^{2}=-\frac{48}{11}$$

The equation is now solved.

$$x=\frac{4\sqrt{33}i}{11} x=-\frac{4\sqrt{33}i}{11}$$

Steps Using the Quadratic Formula

Add -56 and 104 to get 48.

$$11x^{2}+48=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and 48 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\times 48}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\times 48}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\times 48}}{2\times 11}$$

Multiply -44 times 48.

$$x=\frac{0±\sqrt{-2112}}{2\times 11}$$

Take the square root of -2112.

$$x=\frac{0±8\sqrt{33}i}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±8\sqrt{33}i}{22}$$

Now solve the equation x=\frac{0±8\sqrt{33}i}{22} when ± is plus.

$$x=\frac{4\sqrt{33}i}{11}$$

Now solve the equation x=\frac{0±8\sqrt{33}i}{22} when ± is minus.

$$x=-\frac{4\sqrt{33}i}{11}$$

The equation is now solved.

$$x=\frac{4\sqrt{33}i}{11} x=-\frac{4\sqrt{33}i}{11}$$