Solve x^2/9=81

$$\frac { x ^ { 2 } } { 9 } = 81$$

Solve for x

$$x=27$$

$$x=-27$$

Steps Using Difference of Squares

Multiply both sides by 9.

$$x^{2}=81\times 9$$

Multiply 81 and 9 to get 729.

$$x^{2}=729$$

Subtract 729 from both sides.

$$x^{2}-729=0$$

Consider x^{2}-729. Rewrite x^{2}-729 as x^{2}-27^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-27\right)\left(x+27\right)=0$$

To find equation solutions, solve x-27=0 and x+27=0.

$$x=27 x=-27$$

Steps by Finding Square Root

Multiply both sides by 9.

$$x^{2}=81\times 9$$

Multiply 81 and 9 to get 729.

$$x^{2}=729$$

Take the square root of both sides of the equation.

$$x=27 x=-27$$

Steps Using the Quadratic Formula

Multiply both sides by 9.

$$x^{2}=81\times 9$$

Multiply 81 and 9 to get 729.

$$x^{2}=729$$

Subtract 729 from both sides.

$$x^{2}-729=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -729 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-729\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-729\right)}}{2}$$

Multiply -4 times -729.

$$x=\frac{0±\sqrt{2916}}{2}$$

Take the square root of 2916.

$$x=\frac{0±54}{2}$$

Now solve the equation x=\frac{0±54}{2} when ± is plus. Divide 54 by 2.

$$x=27$$

Now solve the equation x=\frac{0±54}{2} when ± is minus. Divide -54 by 2.

$$x=-27$$

The equation is now solved.

$$x=27 x=-27$$