Solve x^2=4sqrt{3}-21.861^2

$${ x }^{ 2 } = 4 \sqrt{ 3 } -2 { 1.861 }^{ 2 }$$

Solve for x (complex solution)

$$x=-\sqrt{4\sqrt{3}-6.926642}\approx -0.039512407$$

$$x=\sqrt{4\sqrt{3}-6.926642}\approx 0.039512407$$

Steps by Finding Square Root

Calculate 1.861 to the power of 2 and get 3.463321.

$$x^{2}=4\sqrt{3}-2\times 3.463321$$

Multiply 2 and 3.463321 to get 6.926642.

$$x^{2}=4\sqrt{3}-6.926642$$

The equation is now solved.

$$x=\sqrt{4\sqrt{3}-6.926642} x=-\sqrt{4\sqrt{3}-6.926642}$$

Steps Using the Quadratic Formula

Calculate 1.861 to the power of 2 and get 3.463321.

$$x^{2}=4\sqrt{3}-2\times 3.463321$$

Multiply 2 and 3.463321 to get 6.926642.

$$x^{2}=4\sqrt{3}-6.926642$$

Subtract 4\sqrt{3} from both sides.

$$x^{2}-4\sqrt{3}=-6.926642$$

Add 6.926642 to both sides.

$$x^{2}-4\sqrt{3}+6.926642=0$$

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.

$$x^{2}+6.926642-4\sqrt{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -4\sqrt{3}+6.926642 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(6.926642-4\sqrt{3}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(6.926642-4\sqrt{3}\right)}}{2}$$

Multiply -4 times -4\sqrt{3}+6.926642.

$$x=\frac{0±\sqrt{16\sqrt{3}-27.706568}}{2}$$

Now solve the equation x=\frac{0±\sqrt{16\sqrt{3}-27.706568}}{2} when ± is plus.

$$x=\frac{\sqrt{16\sqrt{3}-27.706568}}{2}$$

Now solve the equation x=\frac{0±\sqrt{16\sqrt{3}-27.706568}}{2} when ± is minus.

$$x=-\frac{\sqrt{16\sqrt{3}-27.706568}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{16\sqrt{3}-27.706568}}{2} x=-\frac{\sqrt{16\sqrt{3}-27.706568}}{2}$$

Solve for x

$$x=\frac{\sqrt{16\sqrt{3}-27.706568}}{2}\approx 0.039512407$$

$$x=-\frac{\sqrt{16\sqrt{3}-27.706568}}{2}\approx -0.039512407$$