Solve 4x^2+6=10-2x^2

$$4 { x }^{ 2 } +6 = 10-2 { x }^{ 2 }$$

Solve for x

$$x=\frac{\sqrt{6}}{3}\approx 0.816496581$$

$$x=-\frac{\sqrt{6}}{3}\approx -0.816496581$$

Steps by Finding Square Root

Add 2x^{2} to both sides.

$$4x^{2}+6+2x^{2}=10$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}+6=10$$

Subtract 6 from both sides.

$$6x^{2}=10-6$$

Subtract 6 from 10 to get 4.

$$6x^{2}=4$$

Divide both sides by 6.

$$x^{2}=\frac{4}{6}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

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

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$

Steps Using the Quadratic Formula

Subtract 10 from both sides.

$$4x^{2}+6-10=-2x^{2}$$

Subtract 10 from 6 to get -4.

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

Add 2x^{2} to both sides.

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

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$6x^{2}-4=0$$

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

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

Square 0.

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

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\left(-4\right)}}{2\times 6}$$

Multiply -24 times -4.

$$x=\frac{0±\sqrt{96}}{2\times 6}$$

Take the square root of 96.

$$x=\frac{0±4\sqrt{6}}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±4\sqrt{6}}{12}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{12} when ± is plus.

$$x=\frac{\sqrt{6}}{3}$$

Now solve the equation x=\frac{0±4\sqrt{6}}{12} when ± is minus.

$$x=-\frac{\sqrt{6}}{3}$$

The equation is now solved.

$$x=\frac{\sqrt{6}}{3} x=-\frac{\sqrt{6}}{3}$$