Solve 2x^2-8x^2+3=0

$$2 x ^ { 2 } - 8 x ^ { 2 } + 3 = 0$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-6x^{2}=-3$$

Divide both sides by -6.

$$x^{2}=\frac{-3}{-6}$$

Reduce the fraction \frac{-3}{-6} to lowest terms by extracting and canceling out -3.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{2}}{2} x=-\frac{\sqrt{2}}{2}$$

Steps Using the Quadratic Formula

Combine 2x^{2} and -8x^{2} to get -6x^{2}.

$$-6x^{2}+3=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -6 for a, 0 for b, and 3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-6\right)\times 3}}{2\left(-6\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-6\right)\times 3}}{2\left(-6\right)}$$

Multiply -4 times -6.

$$x=\frac{0±\sqrt{24\times 3}}{2\left(-6\right)}$$

Multiply 24 times 3.

$$x=\frac{0±\sqrt{72}}{2\left(-6\right)}$$

Take the square root of 72.

$$x=\frac{0±6\sqrt{2}}{2\left(-6\right)}$$

Multiply 2 times -6.

$$x=\frac{0±6\sqrt{2}}{-12}$$

Now solve the equation x=\frac{0±6\sqrt{2}}{-12} when ± is plus.

$$x=-\frac{\sqrt{2}}{2}$$

Now solve the equation x=\frac{0±6\sqrt{2}}{-12} when ± is minus.

$$x=\frac{\sqrt{2}}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{2}}{2} x=\frac{\sqrt{2}}{2}$$