Solve 5=1/2*20*x^2+1/2*50(x+02)^2

$$5 = \frac { 1 } { 2 } \cdot 20 \cdot x ^ { 2 } + \frac { 1 } { 2 } \cdot 50 ( x + 02 ) ^ { 2 }$$

Solve for x

$$x=\frac{\sqrt{7}}{7}\approx 0.377964473$$

$$x=-\frac{\sqrt{7}}{7}\approx -0.377964473$$

Steps by Finding Square Root

Multiply \frac{1}{2} and 20 to get 10.

$$5=10x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

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

$$5=10x^{2}+25\left(x+0\times 2\right)^{2}$$

Multiply 0 and 2 to get 0.

$$5=10x^{2}+25\left(x+0\right)^{2}$$

Anything plus zero gives itself.

$$5=10x^{2}+25x^{2}$$

Combine 10x^{2} and 25x^{2} to get 35x^{2}.

$$5=35x^{2}$$

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

$$35x^{2}=5$$

Divide both sides by 35.

$$x^{2}=\frac{5}{35}$$

Reduce the fraction \frac{5}{35} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{1}{7}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{7}}{7} x=-\frac{\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Multiply \frac{1}{2} and 20 to get 10.

$$5=10x^{2}+\frac{1}{2}\times 50\left(x+0\times 2\right)^{2}$$

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

$$5=10x^{2}+25\left(x+0\times 2\right)^{2}$$

Multiply 0 and 2 to get 0.

$$5=10x^{2}+25\left(x+0\right)^{2}$$

Anything plus zero gives itself.

$$5=10x^{2}+25x^{2}$$

Combine 10x^{2} and 25x^{2} to get 35x^{2}.

$$5=35x^{2}$$

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

$$35x^{2}=5$$

Subtract 5 from both sides.

$$35x^{2}-5=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 35 for a, 0 for b, and -5 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 35\left(-5\right)}}{2\times 35}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 35\left(-5\right)}}{2\times 35}$$

Multiply -4 times 35.

$$x=\frac{0±\sqrt{-140\left(-5\right)}}{2\times 35}$$

Multiply -140 times -5.

$$x=\frac{0±\sqrt{700}}{2\times 35}$$

Take the square root of 700.

$$x=\frac{0±10\sqrt{7}}{2\times 35}$$

Multiply 2 times 35.

$$x=\frac{0±10\sqrt{7}}{70}$$

Now solve the equation x=\frac{0±10\sqrt{7}}{70} when ± is plus.

$$x=\frac{\sqrt{7}}{7}$$

Now solve the equation x=\frac{0±10\sqrt{7}}{70} when ± is minus.

$$x=-\frac{\sqrt{7}}{7}$$

The equation is now solved.

$$x=\frac{\sqrt{7}}{7} x=-\frac{\sqrt{7}}{7}$$