Solve x^2-5^2=-7

$$x ^ { 2 } - 5 ^ { 2 } = - 7$$

Solve for x

$$x=3\sqrt{2}\approx 4.242640687$$

$$x=-3\sqrt{2}\approx -4.242640687$$

Steps by Finding Square Root

Calculate 5 to the power of 2 and get 25.

$$x^{2}-25=-7$$

Add 25 to both sides.

$$x^{2}=-7+25$$

Add -7 and 25 to get 18.

$$x^{2}=18$$

Take the square root of both sides of the equation.

$$x=3\sqrt{2} x=-3\sqrt{2}$$

Steps Using the Quadratic Formula

Calculate 5 to the power of 2 and get 25.

$$x^{2}-25=-7$$

Add 7 to both sides.

$$x^{2}-25+7=0$$

Add -25 and 7 to get -18.

$$x^{2}-18=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -18 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-18\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-18\right)}}{2}$$

Multiply -4 times -18.

$$x=\frac{0±\sqrt{72}}{2}$$

Take the square root of 72.

$$x=\frac{0±6\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{2}}{2} when ± is plus.

$$x=3\sqrt{2}$$

Now solve the equation x=\frac{0±6\sqrt{2}}{2} when ± is minus.

$$x=-3\sqrt{2}$$

The equation is now solved.

$$x=3\sqrt{2} x=-3\sqrt{2}$$