Solve 27x^2=27^2

$$27 x ^ { 2 } = 27 ^ { 2 }$$

Solve for x

$$x=3\sqrt{3}\approx 5.196152423$$

$$x=-3\sqrt{3}\approx -5.196152423$$

Steps by Finding Square Root

Calculate 27 to the power of 2 and get 729.

$$27x^{2}=729$$

Divide both sides by 27.

$$x^{2}=\frac{729}{27}$$

Divide 729 by 27 to get 27.

$$x^{2}=27$$

Take the square root of both sides of the equation.

$$x=3\sqrt{3} x=-3\sqrt{3}$$

Steps Using the Quadratic Formula

Calculate 27 to the power of 2 and get 729.

$$27x^{2}=729$$

Subtract 729 from both sides.

$$27x^{2}-729=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 27 for a, 0 for b, and -729 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 27\left(-729\right)}}{2\times 27}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 27\left(-729\right)}}{2\times 27}$$

Multiply -4 times 27.

$$x=\frac{0±\sqrt{-108\left(-729\right)}}{2\times 27}$$

Multiply -108 times -729.

$$x=\frac{0±\sqrt{78732}}{2\times 27}$$

Take the square root of 78732.

$$x=\frac{0±162\sqrt{3}}{2\times 27}$$

Multiply 2 times 27.

$$x=\frac{0±162\sqrt{3}}{54}$$

Now solve the equation x=\frac{0±162\sqrt{3}}{54} when ± is plus.

$$x=3\sqrt{3}$$

Now solve the equation x=\frac{0±162\sqrt{3}}{54} when ± is minus.

$$x=-3\sqrt{3}$$

The equation is now solved.

$$x=3\sqrt{3} x=-3\sqrt{3}$$