Solve 25m^2+10m^2+1-32m^2-32=0

$$25 m ^ { 2 } + 10 m ^ { 2 } + 1 - 32 m ^ { 2 } - 32 = 0$$

Solve for m

$$m = \frac{\sqrt{93}}{3} \approx 3.214550254$$

$$m = -\frac{\sqrt{93}}{3} \approx -3.214550254$$

Steps by Finding Square Root

Combine 25m^{2} and 10m^{2} to get 35m^{2}.

$$35m^{2}+1-32m^{2}-32=0$$

Combine 35m^{2} and -32m^{2} to get 3m^{2}.

$$3m^{2}+1-32=0$$

Subtract 32 from 1 to get -31.

$$3m^{2}-31=0$$

Add 31 to both sides. Anything plus zero gives itself.

$$3m^{2}=31$$

Divide both sides by 3.

$$m^{2}=\frac{31}{3}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{93}}{3} m=-\frac{\sqrt{93}}{3}$$

Steps Using the Quadratic Formula

Combine 25m^{2} and 10m^{2} to get 35m^{2}.

$$35m^{2}+1-32m^{2}-32=0$$

Combine 35m^{2} and -32m^{2} to get 3m^{2}.

$$3m^{2}+1-32=0$$

Subtract 32 from 1 to get -31.

$$3m^{2}-31=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -31 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 3\left(-31\right)}}{2\times 3}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 3\left(-31\right)}}{2\times 3}$$

Multiply -4 times 3.

$$m=\frac{0±\sqrt{-12\left(-31\right)}}{2\times 3}$$

Multiply -12 times -31.

$$m=\frac{0±\sqrt{372}}{2\times 3}$$

Take the square root of 372.

$$m=\frac{0±2\sqrt{93}}{2\times 3}$$

Multiply 2 times 3.

$$m=\frac{0±2\sqrt{93}}{6}$$

Now solve the equation m=\frac{0±2\sqrt{93}}{6} when ± is plus.

$$m=\frac{\sqrt{93}}{3}$$

Now solve the equation m=\frac{0±2\sqrt{93}}{6} when ± is minus.

$$m=-\frac{\sqrt{93}}{3}$$

The equation is now solved.

$$m=\frac{\sqrt{93}}{3} m=-\frac{\sqrt{93}}{3}$$