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

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

Solve for x

$$x=10\sqrt{3}\approx 17.320508076$$

$$x=-10\sqrt{3}\approx -17.320508076$$

Steps by Finding Square Root

Expand \left(10\sqrt{3}\right)^{2}.

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

Calculate 10 to the power of 2 and get 100.

$$x^{2}+100\left(\sqrt{3}\right)^{2}=2x^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}+100\times 3=2x^{2}$$

Multiply 100 and 3 to get 300.

$$x^{2}+300=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+300-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+300=0$$

Subtract 300 from both sides. Anything subtracted from zero gives its negation.

$$-x^{2}=-300$$

Divide both sides by -1.

$$x^{2}=\frac{-300}{-1}$$

Fraction \frac{-300}{-1} can be simplified to 300 by removing the negative sign from both the numerator and the denominator.

$$x^{2}=300$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Expand \left(10\sqrt{3}\right)^{2}.

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

Calculate 10 to the power of 2 and get 100.

$$x^{2}+100\left(\sqrt{3}\right)^{2}=2x^{2}$$

The square of \sqrt{3} is 3.

$$x^{2}+100\times 3=2x^{2}$$

Multiply 100 and 3 to get 300.

$$x^{2}+300=2x^{2}$$

Subtract 2x^{2} from both sides.

$$x^{2}+300-2x^{2}=0$$

Combine x^{2} and -2x^{2} to get -x^{2}.

$$-x^{2}+300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 300}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\times 300}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\times 300}}{2\left(-1\right)}$$

Multiply 4 times 300.

$$x=\frac{0±\sqrt{1200}}{2\left(-1\right)}$$

Take the square root of 1200.

$$x=\frac{0±20\sqrt{3}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±20\sqrt{3}}{-2}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{-2} when ± is plus.

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

Now solve the equation x=\frac{0±20\sqrt{3}}{-2} when ± is minus.

$$x=10\sqrt{3}$$

The equation is now solved.

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