Solve 2x^2+100^2-250^2=0

$$2 x ^ { 2 } + 100 ^ { 2 } - 250 ^ { 2 } = 0$$

Solve for x

$$x=25\sqrt{42}\approx 162.01851746$$

$$x=-25\sqrt{42}\approx -162.01851746$$

Steps by Finding Square Root

Calculate 100 to the power of 2 and get 10000.

$$2x^{2}[phone]^{2}=0$$

Calculate 250 to the power of 2 and get 62500.

$$2x^{2}[phone]=0$$

Subtract 62500 from 10000 to get -52500.

$$2x^{2}-52500=0$$

Add 52500 to both sides. Anything plus zero gives itself.

$$2x^{2}=52500$$

Divide both sides by 2.

$$x^{2}=\frac{52500}{2}$$

Divide 52500 by 2 to get 26250.

$$x^{2}=26250$$

Take the square root of both sides of the equation.

$$x=25\sqrt{42} x=-25\sqrt{42}$$

Steps Using the Quadratic Formula

Calculate 100 to the power of 2 and get 10000.

$$2x^{2}[phone]^{2}=0$$

Calculate 250 to the power of 2 and get 62500.

$$2x^{2}[phone]=0$$

Subtract 62500 from 10000 to get -52500.

$$2x^{2}-52500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -52500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-52500\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-52500\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-52500\right)}}{2\times 2}$$

Multiply -8 times -52500.

$$x=\frac{0±\sqrt{420000}}{2\times 2}$$

Take the square root of 420000.

$$x=\frac{0±100\sqrt{42}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±100\sqrt{42}}{4}$$

Now solve the equation x=\frac{0±100\sqrt{42}}{4} when ± is plus.

$$x=25\sqrt{42}$$

Now solve the equation x=\frac{0±100\sqrt{42}}{4} when ± is minus.

$$x=-25\sqrt{42}$$

The equation is now solved.

$$x=25\sqrt{42} x=-25\sqrt{42}$$