Solve 11x^2+126=0

$$11 { x }^{ 2 } +126=0$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{154}i}{11}\approx -0-3.384456449i$$

$$x=\frac{3\sqrt{154}i}{11}\approx 3.384456449i$$

Steps by Finding Square Root

Subtract 126 from both sides. Anything subtracted from zero gives its negation.

$$11x^{2}=-126$$

Divide both sides by 11.

$$x^{2}=-\frac{126}{11}$$

The equation is now solved.

$$x=\frac{3\sqrt{154}i}{11} x=-\frac{3\sqrt{154}i}{11}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$11x^{2}+126=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and 126 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\times 126}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\times 126}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\times 126}}{2\times 11}$$

Multiply -44 times 126.

$$x=\frac{0±\sqrt{-5544}}{2\times 11}$$

Take the square root of -5544.

$$x=\frac{0±6\sqrt{154}i}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±6\sqrt{154}i}{22}$$

Now solve the equation x=\frac{0±6\sqrt{154}i}{22} when ± is plus.

$$x=\frac{3\sqrt{154}i}{11}$$

Now solve the equation x=\frac{0±6\sqrt{154}i}{22} when ± is minus.

$$x=-\frac{3\sqrt{154}i}{11}$$

The equation is now solved.

$$x=\frac{3\sqrt{154}i}{11} x=-\frac{3\sqrt{154}i}{11}$$