Solve x^2+3=21

$$x ^ { 2 } + 3 = 21$$

Solve for x

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

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

Steps by Finding Square Root

Subtract 3 from both sides.

$$x^{2}=21-3$$

Subtract 3 from 21 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

Subtract 21 from both sides.

$$x^{2}+3-21=0$$

Subtract 21 from 3 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.

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