Solve 2m^2+6m^2=1

$$2 m ^ { 2 } + 6 m ^ { 2 } = 1$$

Solve for m

$$m=\frac{\sqrt{2}}{4}\approx 0.353553391$$

$$m=-\frac{\sqrt{2}}{4}\approx -0.353553391$$

Steps by Finding Square Root

Combine 2m^{2} and 6m^{2} to get 8m^{2}.

$$8m^{2}=1$$

Divide both sides by 8.

$$m^{2}=\frac{1}{8}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{2}}{4} m=-\frac{\sqrt{2}}{4}$$

Steps Using the Quadratic Formula

Combine 2m^{2} and 6m^{2} to get 8m^{2}.

$$8m^{2}=1$$

Subtract 1 from both sides.

$$8m^{2}-1=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 8 for a, 0 for b, and -1 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 8\left(-1\right)}}{2\times 8}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 8\left(-1\right)}}{2\times 8}$$

Multiply -4 times 8.

$$m=\frac{0±\sqrt{-32\left(-1\right)}}{2\times 8}$$

Multiply -32 times -1.

$$m=\frac{0±\sqrt{32}}{2\times 8}$$

Take the square root of 32.

$$m=\frac{0±4\sqrt{2}}{2\times 8}$$

Multiply 2 times 8.

$$m=\frac{0±4\sqrt{2}}{16}$$

Now solve the equation m=\frac{0±4\sqrt{2}}{16} when ± is plus.

$$m=\frac{\sqrt{2}}{4}$$

Now solve the equation m=\frac{0±4\sqrt{2}}{16} when ± is minus.

$$m=-\frac{\sqrt{2}}{4}$$

The equation is now solved.

$$m=\frac{\sqrt{2}}{4} m=-\frac{\sqrt{2}}{4}$$