Solve 5x^2=2^5

$$5 x ^ { 2 } = 2 ^ { 5 }$$

Solve for x

$$x = \frac{4 \sqrt{10}}{5} \approx 2.529822128$$

$$x = -\frac{4 \sqrt{10}}{5} \approx -2.529822128$$

Steps by Finding Square Root

Calculate 2 to the power of 5 and get 32.

$$5x^{2}=32$$

Divide both sides by 5.

$$x^{2}=\frac{32}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{4\sqrt{10}}{5} x=-\frac{4\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

Calculate 2 to the power of 5 and get 32.

$$5x^{2}=32$$

Subtract 32 from both sides.

$$5x^{2}-32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-32\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-32\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-32\right)}}{2\times 5}$$

Multiply -20 times -32.

$$x=\frac{0±\sqrt{640}}{2\times 5}$$

Take the square root of 640.

$$x=\frac{0±8\sqrt{10}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±8\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{10} when ± is plus.

$$x=\frac{4\sqrt{10}}{5}$$

Now solve the equation x=\frac{0±8\sqrt{10}}{10} when ± is minus.

$$x=-\frac{4\sqrt{10}}{5}$$

The equation is now solved.

$$x=\frac{4\sqrt{10}}{5} x=-\frac{4\sqrt{10}}{5}$$