Solve 5=1/2250x^2+1/250left(x+02right)^2

$$5 = \frac{ 1 }{ 2 } 250 { x }^{ 2 } + \frac{ 1 }{ 2 } 50 { \left(x+02 \right) }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{30}}{30}\approx 0.182574186$$

$$x=-\frac{\sqrt{30}}{30}\approx -0.182574186$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 250 to get 125.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

Multiply \frac{1}{2} and 50 to get 25.

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

Multiply 0 and 2 to get 0.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

Anything plus zero gives itself.

$$5=125x^{2}+25x^{2}$$

Combine 125x^{2} and 25x^{2} to get 150x^{2}.

$$5=150x^{2}$$

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

$$150x^{2}=5$$

Divide both sides by 150.

$$x^{2}=\frac{5}{150}$$

Reduce the fraction \frac{5}{150} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{1}{30}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 250 to get 125.

$$5=125x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

Multiply \frac{1}{2} and 50 to get 25.

$$5=125x^{2}+25\left(x+0\times 2\right)^{2}$$

Multiply 0 and 2 to get 0.

$$5=125x^{2}+25\left(x+0\right)^{2}$$

Anything plus zero gives itself.

$$5=125x^{2}+25x^{2}$$

Combine 125x^{2} and 25x^{2} to get 150x^{2}.

$$5=150x^{2}$$

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

$$150x^{2}=5$$

Subtract 5 from both sides.

$$150x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 150 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 150\left(-5\right)}}{2\times 150}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 150\left(-5\right)}}{2\times 150}$$

Multiply -4 times 150.

$$x=\frac{0±\sqrt{-600\left(-5\right)}}{2\times 150}$$

Multiply -600 times -5.

$$x=\frac{0±\sqrt{3000}}{2\times 150}$$

Take the square root of 3000.

$$x=\frac{0±10\sqrt{30}}{2\times 150}$$

Multiply 2 times 150.

$$x=\frac{0±10\sqrt{30}}{300}$$

Now solve the equation x=\frac{0±10\sqrt{30}}{300} when ± is plus.

$$x=\frac{\sqrt{30}}{30}$$

Now solve the equation x=\frac{0±10\sqrt{30}}{300} when ± is minus.

$$x=-\frac{\sqrt{30}}{30}$$

The equation is now solved.

$$x=\frac{\sqrt{30}}{30} x=-\frac{\sqrt{30}}{30}$$