Solve x^2+49-8sqrt{3}=0

$${ x }^{ 2 } +49-8 \sqrt{ 3 } = 0$$

Solve for x (complex solution)

$$x=-4\sqrt{3}i+i\approx -5.92820323i$$

$$x=4\sqrt{3}i-i\approx 5.92820323i$$

Steps by Finding Square Root

Subtract 49 from both sides. Anything subtracted from zero gives its negation.

$$x^{2}-8\sqrt{3}=-49$$

Add 8\sqrt{3} to both sides.

$$x^{2}=-49+8\sqrt{3}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

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.

$$x^{2}+49-8\sqrt{3}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 49-8\sqrt{3} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(49-8\sqrt{3}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(49-8\sqrt{3}\right)}}{2}$$

Multiply -4 times 49-8\sqrt{3}.

$$x=\frac{0±\sqrt{32\sqrt{3}-196}}{2}$$

Take the square root of -196+32\sqrt{3}.

$$x=\frac{0±\left(8\sqrt{3}i-2i\right)}{2}$$

Now solve the equation x=\frac{0±\left(8\sqrt{3}i-2i\right)}{2} when ± is plus.

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

Now solve the equation x=\frac{0±\left(8\sqrt{3}i-2i\right)}{2} when ± is minus.

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

The equation is now solved.

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