Solve 11x^2-99=0

$$11 x ^ { 2 } - 99 = 0$$

Solve for x

$$x=3$$

$$x=-3$$

Steps Using Difference of Squares

Divide both sides by 11.

$$x^{2}-9=0$$

Consider x^{2}-9. Rewrite x^{2}-9 as x^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-3\right)\left(x+3\right)=0$$

To find equation solutions, solve x-3=0 and x+3=0.

$$x=3 x=-3$$

Steps by Finding Square Root

Add 99 to both sides. Anything plus zero gives itself.

$$11x^{2}=99$$

Divide both sides by 11.

$$x^{2}=\frac{99}{11}$$

Divide 99 by 11 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

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.

$$11x^{2}-99=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 11 for a, 0 for b, and -99 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 11\left(-99\right)}}{2\times 11}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 11\left(-99\right)}}{2\times 11}$$

Multiply -4 times 11.

$$x=\frac{0±\sqrt{-44\left(-99\right)}}{2\times 11}$$

Multiply -44 times -99.

$$x=\frac{0±\sqrt{4356}}{2\times 11}$$

Take the square root of 4356.

$$x=\frac{0±66}{2\times 11}$$

Multiply 2 times 11.

$$x=\frac{0±66}{22}$$

Now solve the equation x=\frac{0±66}{22} when ± is plus. Divide 66 by 22.

$$x=3$$

Now solve the equation x=\frac{0±66}{22} when ± is minus. Divide -66 by 22.

$$x=-3$$

The equation is now solved.

$$x=3 x=-3$$