Solve x^2=36/121

$$x ^ { 2 } = \frac { 36 } { 121 }$$

Solve for x

$$x=\frac{6}{11}\approx 0.545454545$$

$$x=-\frac{6}{11}\approx -0.545454545$$

Steps Using Difference of Squares

Subtract \frac{36}{121} from both sides.

$$x^{2}-\frac{36}{121}=0$$

Multiply both sides by 121.

$$121x^{2}-36=0$$

Consider 121x^{2}-36. Rewrite 121x^{2}-36 as \left(11x\right)^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(11x-6\right)\left(11x+6\right)=0$$

To find equation solutions, solve 11x-6=0 and 11x+6=0.

$$x=\frac{6}{11} x=-\frac{6}{11}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$x=\frac{6}{11} x=-\frac{6}{11}$$

Steps Using the Quadratic Formula

Subtract \frac{36}{121} from both sides.

$$x^{2}-\frac{36}{121}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{36}{121} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{36}{121}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{36}{121}\right)}}{2}$$

Multiply -4 times -\frac{36}{121}.

$$x=\frac{0±\sqrt{\frac{144}{121}}}{2}$$

Take the square root of \frac{144}{121}.

$$x=\frac{0±\frac{12}{11}}{2}$$

Now solve the equation x=\frac{0±\frac{12}{11}}{2} when ± is plus.

$$x=\frac{6}{11}$$

Now solve the equation x=\frac{0±\frac{12}{11}}{2} when ± is minus.

$$x=-\frac{6}{11}$$

The equation is now solved.

$$x=\frac{6}{11} x=-\frac{6}{11}$$