Solve x^2=4sqrt{3}-10

$$x ^ { 2 } = 4 \sqrt { 3 } - 10$$

Solve for x (complex solution)

$$x=-i\sqrt{10-4\sqrt{3}}\approx -0-1.752654207i$$

$$x=i\sqrt{10-4\sqrt{3}}\approx 1.752654207i$$

Steps by Finding Square Root

The equation is now solved.

$$x=i\sqrt{10-4\sqrt{3}} x=-i\sqrt{10-4\sqrt{3}}$$

Steps Using the Quadratic Formula

Subtract 4\sqrt{3} from both sides.

$$x^{2}-4\sqrt{3}=-10$$

Add 10 to both sides.

$$x^{2}-4\sqrt{3}+10=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$x^{2}+10-4\sqrt{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4\sqrt{3}+10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(10-4\sqrt{3}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(10-4\sqrt{3}\right)}}{2}$$

Multiply -4 times -4\sqrt{3}+10.

$$x=\frac{0±\sqrt{16\sqrt{3}-40}}{2}$$

Take the square root of 16\sqrt{3}-40.

$$x=\frac{0±2i\sqrt{10-4\sqrt{3}}}{2}$$

Now solve the equation x=\frac{0±2i\sqrt{10-4\sqrt{3}}}{2} when ± is plus.

$$x=i\sqrt{10-4\sqrt{3}}$$

Now solve the equation x=\frac{0±2i\sqrt{10-4\sqrt{3}}}{2} when ± is minus.

$$x=-i\sqrt{10-4\sqrt{3}}$$

The equation is now solved.

$$x=i\sqrt{10-4\sqrt{3}} x=-i\sqrt{10-4\sqrt{3}}$$