Solve x^2+7=22

$$x ^ { 2 } + 7 = 22$$

Solve for x

$$x=\sqrt{15}\approx 3.872983346$$

$$x=-\sqrt{15}\approx -3.872983346$$

Steps by Finding Square Root

Subtract 7 from both sides.

$$x^{2}=22-7$$

Subtract 7 from 22 to get 15.

$$x^{2}=15$$

Take the square root of both sides of the equation.

$$x=\sqrt{15} x=-\sqrt{15}$$

Steps Using the Quadratic Formula

Subtract 22 from both sides.

$$x^{2}+7-22=0$$

Subtract 22 from 7 to get -15.

$$x^{2}-15=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -15 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-15\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-15\right)}}{2}$$

Multiply -4 times -15.

$$x=\frac{0±\sqrt{60}}{2}$$

Take the square root of 60.

$$x=\frac{0±2\sqrt{15}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{2} when ± is plus.

$$x=\sqrt{15}$$

Now solve the equation x=\frac{0±2\sqrt{15}}{2} when ± is minus.

$$x=-\sqrt{15}$$

The equation is now solved.

$$x=\sqrt{15} x=-\sqrt{15}$$