Solve a^2=25/121

$$a ^ { 2 } = \frac { 25 } { 121 }$$

Solve for a

$$a=\frac{5}{11}\approx 0.454545455$$

$$a=-\frac{5}{11}\approx -0.454545455$$

Steps Using Difference of Squares

Subtract \frac{25}{121} from both sides.

$$a^{2}-\frac{25}{121}=0$$

Multiply both sides by 121.

$$121a^{2}-25=0$$

Consider 121a^{2}-25. Rewrite 121a^{2}-25 as \left(11a\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(11a-5\right)\left(11a+5\right)=0$$

To find equation solutions, solve 11a-5=0 and 11a+5=0.

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Steps by Finding Square Root

Take the square root of both sides of the equation.

$$a=\frac{5}{11} a=-\frac{5}{11}$$

Steps Using the Quadratic Formula

Subtract \frac{25}{121} from both sides.

$$a^{2}-\frac{25}{121}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{25}{121} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$a=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{121}\right)}}{2}$$

Square 0.

$$a=\frac{0±\sqrt{-4\left(-\frac{25}{121}\right)}}{2}$$

Multiply -4 times -\frac{25}{121}.

$$a=\frac{0±\sqrt{\frac{100}{121}}}{2}$$

Take the square root of \frac{100}{121}.

$$a=\frac{0±\frac{10}{11}}{2}$$

Now solve the equation a=\frac{0±\frac{10}{11}}{2} when ± is plus.

$$a=\frac{5}{11}$$

Now solve the equation a=\frac{0±\frac{10}{11}}{2} when ± is minus.

$$a=-\frac{5}{11}$$

The equation is now solved.

$$a=\frac{5}{11} a=-\frac{5}{11}$$