Solve 4x^2=2-x^2

$$4 { x }^{ 2 } =2- { x }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{10}}{5}\approx 0.632455532$$

$$x=-\frac{\sqrt{10}}{5}\approx -0.632455532$$

Steps by Finding Square Root

Add x^{2} to both sides.

$$4x^{2}+x^{2}=2$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

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

Divide both sides by 5.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}$$

Steps Using the Quadratic Formula

Subtract 2 from both sides.

$$4x^{2}-2=-x^{2}$$

Add x^{2} to both sides.

$$4x^{2}-2+x^{2}=0$$

Combine 4x^{2} and x^{2} to get 5x^{2}.

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

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

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

Square 0.

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

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-2\right)}}{2\times 5}$$

Multiply -20 times -2.

$$x=\frac{0±\sqrt{40}}{2\times 5}$$

Take the square root of 40.

$$x=\frac{0±2\sqrt{10}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±2\sqrt{10}}{10}$$

Now solve the equation x=\frac{0±2\sqrt{10}}{10} when ± is plus.

$$x=\frac{\sqrt{10}}{5}$$

Now solve the equation x=\frac{0±2\sqrt{10}}{10} when ± is minus.

$$x=-\frac{\sqrt{10}}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{10}}{5} x=-\frac{\sqrt{10}}{5}$$