Solve x^2=(2sqrt{3})^2+10

$$x ^ { 2 } = ( 2 \sqrt { 3 } ) ^ { 2 } + 10$$

Solve for x

$$x=\sqrt{22}\approx 4.69041576$$

$$x=-\sqrt{22}\approx -4.69041576$$

Steps by Finding Square Root

Expand \left(2\sqrt{3}\right)^{2}.

$$x^{2}=2^{2}\left(\sqrt{3}\right)^{2}+10$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=4\left(\sqrt{3}\right)^{2}+10$$

The square of \sqrt{3} is 3.

$$x^{2}=4\times 3+10$$

Multiply 4 and 3 to get 12.

$$x^{2}=12+10$$

Add 12 and 10 to get 22.

$$x^{2}=22$$

Take the square root of both sides of the equation.

$$x=\sqrt{22} x=-\sqrt{22}$$

Steps Using the Quadratic Formula

Expand \left(2\sqrt{3}\right)^{2}.

$$x^{2}=2^{2}\left(\sqrt{3}\right)^{2}+10$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}=4\left(\sqrt{3}\right)^{2}+10$$

The square of \sqrt{3} is 3.

$$x^{2}=4\times 3+10$$

Multiply 4 and 3 to get 12.

$$x^{2}=12+10$$

Add 12 and 10 to get 22.

$$x^{2}=22$$

Subtract 22 from both sides.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-22\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-22\right)}}{2}$$

Multiply -4 times -22.

$$x=\frac{0±\sqrt{88}}{2}$$

Take the square root of 88.

$$x=\frac{0±2\sqrt{22}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{2} when ± is plus.

$$x=\sqrt{22}$$

Now solve the equation x=\frac{0±2\sqrt{22}}{2} when ± is minus.

$$x=-\sqrt{22}$$

The equation is now solved.

$$x=\sqrt{22} x=-\sqrt{22}$$