Solve -x^2-4x^2+2=0

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

Solve for x

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

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

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

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

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

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

Divide both sides by -5.

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

Fraction \frac{-2}{-5} can be simplified to \frac{2}{5} by removing the negative sign from both the numerator and the denominator.

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

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

Combine -x^{2} and -4x^{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}.

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

Square 0.

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

Multiply -4 times -5.

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

Multiply 20 times 2.

$$x=\frac{0±\sqrt{40}}{2\left(-5\right)}$$

Take the square root of 40.

$$x=\frac{0±2\sqrt{10}}{2\left(-5\right)}$$

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.

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