Solve 0=81x^2-121

$$0 = 81 x ^ { 2 } - 121$$

Solve for x

$$x = \frac{11}{9} = 1\frac{2}{9} \approx 1.222222222$$

$$x = -\frac{11}{9} = -1\frac{2}{9} \approx -1.222222222$$

Steps Using Difference of Squares

Swap sides so that all variable terms are on the left hand side.

$$81x^{2}-121=0$$

Consider 81x^{2}-121. Rewrite 81x^{2}-121 as \left(9x\right)^{2}-11^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(9x-11\right)\left(9x+11\right)=0$$

To find equation solutions, solve 9x-11=0 and 9x+11=0.

$$x=\frac{11}{9} x=-\frac{11}{9}$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$81x^{2}-121=0$$

Add 121 to both sides. Anything plus zero gives itself.

$$81x^{2}=121$$

Divide both sides by 81.

$$x^{2}=\frac{121}{81}$$

Take the square root of both sides of the equation.

$$x=\frac{11}{9} x=-\frac{11}{9}$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$81x^{2}-121=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 81 for a, 0 for b, and -121 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 81\left(-121\right)}}{2\times 81}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 81\left(-121\right)}}{2\times 81}$$

Multiply -4 times 81.

$$x=\frac{0±\sqrt{-324\left(-121\right)}}{2\times 81}$$

Multiply -324 times -121.

$$x=\frac{0±\sqrt{39204}}{2\times 81}$$

Take the square root of 39204.

$$x=\frac{0±198}{2\times 81}$$

Multiply 2 times 81.

$$x=\frac{0±198}{162}$$

Now solve the equation x=\frac{0±198}{162} when ± is plus. Reduce the fraction \frac{198}{162} to lowest terms by extracting and canceling out 18.

$$x=\frac{11}{9}$$

Now solve the equation x=\frac{0±198}{162} when ± is minus. Reduce the fraction \frac{-198}{162} to lowest terms by extracting and canceling out 18.

$$x=-\frac{11}{9}$$

The equation is now solved.

$$x=\frac{11}{9} x=-\frac{11}{9}$$