Solve x^2+3=24

$$x ^ { 2 } + 3 = 24$$

Solve for x

$$x=\sqrt{21}\approx 4.582575695$$

$$x=-\sqrt{21}\approx -4.582575695$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$x^{2}=24-3$$

Subtract 3 from 24 to get 21.

$$x^{2}=21$$

Take the square root of both sides of the equation.

$$x=\sqrt{21} x=-\sqrt{21}$$

Steps Using the Quadratic Formula

Subtract 24 from both sides.

$$x^{2}+3-24=0$$

Subtract 24 from 3 to get -21.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -21 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-21\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-21\right)}}{2}$$

Multiply -4 times -21.

$$x=\frac{0±\sqrt{84}}{2}$$

Take the square root of 84.

$$x=\frac{0±2\sqrt{21}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{2} when ± is plus.

$$x=\sqrt{21}$$

Now solve the equation x=\frac{0±2\sqrt{21}}{2} when ± is minus.

$$x=-\sqrt{21}$$

The equation is now solved.

$$x=\sqrt{21} x=-\sqrt{21}$$