Solve x^2+x^2+x^2=10000

$${ x }^{ 2 } + { x }^{ 2 } + { x }^{ 2 } =10000$$

Solve for x

$$x = \frac{100 \sqrt{3}}{3} \approx 57.735026919$$

$$x = -\frac{100 \sqrt{3}}{3} \approx -57.735026919$$

Steps by Finding Square Root

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

$$2x^{2}+x^{2}=10000$$

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

$$3x^{2}=10000$$

Divide both sides by 3.

$$x^{2}=\frac{10000}{3}$$

Take the square root of both sides of the equation.

$$x=\frac{100\sqrt{3}}{3} x=-\frac{100\sqrt{3}}{3}$$

Steps Using the Quadratic Formula

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

$$2x^{2}+x^{2}=10000$$

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

$$3x^{2}=10000$$

Subtract 10000 from both sides.

$$3x^{2}-10000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -10000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-10000\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-10000\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-10000\right)}}{2\times 3}$$

Multiply -12 times -10000.

$$x=\frac{0±\sqrt{120000}}{2\times 3}$$

Take the square root of 120000.

$$x=\frac{0±200\sqrt{3}}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±200\sqrt{3}}{6}$$

Now solve the equation x=\frac{0±200\sqrt{3}}{6} when ± is plus.

$$x=\frac{100\sqrt{3}}{3}$$

Now solve the equation x=\frac{0±200\sqrt{3}}{6} when ± is minus.

$$x=-\frac{100\sqrt{3}}{3}$$

The equation is now solved.

$$x=\frac{100\sqrt{3}}{3} x=-\frac{100\sqrt{3}}{3}$$