Solve 7x^2=625

$$7 x ^ { 2 } = 625$$

Solve for x

$$x = \frac{25 \sqrt{7}}{7} \approx 9.449111825$$

$$x = -\frac{25 \sqrt{7}}{7} \approx -9.449111825$$

Steps by Finding Square Root

Divide both sides by 7.

$$x^{2}=\frac{625}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{25\sqrt{7}}{7} x=-\frac{25\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 7.

$$x^{2}=\frac{625}{7}$$

Subtract \frac{625}{7} from both sides.

$$x^{2}-\frac{625}{7}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{625}{7} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{625}{7}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{625}{7}\right)}}{2}$$

Multiply -4 times -\frac{625}{7}.

$$x=\frac{0±\sqrt{\frac{2500}{7}}}{2}$$

Take the square root of \frac{2500}{7}.

$$x=\frac{0±\frac{50\sqrt{7}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{50\sqrt{7}}{7}}{2} when ± is plus.

$$x=\frac{25\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±\frac{50\sqrt{7}}{7}}{2} when ± is minus.

$$x=-\frac{25\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{25\sqrt{7}}{7} x=-\frac{25\sqrt{7}}{7}$$