Solve 10^2=2x^2+x^2

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

Solve for x

$$x = \frac{10 \sqrt{3}}{3} \approx 5.773502692$$

$$x = -\frac{10 \sqrt{3}}{3} \approx -5.773502692$$

Steps by Finding Square Root

Calculate 10 to the power of 2 and get 100.

$$100=2x^{2}+x^{2}$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$100=3x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}=100$$

Divide both sides by 3.

$$x^{2}=\frac{100}{3}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Calculate 10 to the power of 2 and get 100.

$$100=2x^{2}+x^{2}$$

Combine 2x^{2} and x^{2} to get 3x^{2}.

$$100=3x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$3x^{2}=100$$

Subtract 100 from both sides.

$$3x^{2}-100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-100\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-100\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-100\right)}}{2\times 3}$$

Multiply -12 times -100.

$$x=\frac{0±\sqrt{1200}}{2\times 3}$$

Take the square root of 1200.

$$x=\frac{0±20\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±20\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±20\sqrt{3}}{6} when ± is plus.

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

Now solve the equation x=\frac{0±20\sqrt{3}}{6} when ± is minus.

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

The equation is now solved.

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