Solve m^2-8m^2+16=0

$$m ^ { 2 } - 8 m ^ { 2 } + 16 = 0$$

Solve for m

$$m = \frac{4 \sqrt{7}}{7} \approx 1.511857892$$

$$m = -\frac{4 \sqrt{7}}{7} \approx -1.511857892$$

Steps by Finding Square Root

Combine m^{2} and -8m^{2} to get -7m^{2}.

$$-7m^{2}+16=0$$

Subtract 16 from both sides. Anything subtracted from zero gives its negation.

$$-7m^{2}=-16$$

Divide both sides by -7.

$$m^{2}=\frac{-16}{-7}$$

Fraction \frac{-16}{-7} can be simplified to \frac{16}{7} by removing the negative sign from both the numerator and the denominator.

$$m^{2}=\frac{16}{7}$$

Take the square root of both sides of the equation.

$$m=\frac{4\sqrt{7}}{7} m=-\frac{4\sqrt{7}}{7}$$

Steps Using the Quadratic Formula

Combine m^{2} and -8m^{2} to get -7m^{2}.

$$-7m^{2}+16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -7 for a, 0 for b, and 16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-7\right)\times 16}}{2\left(-7\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-7\right)\times 16}}{2\left(-7\right)}$$

Multiply -4 times -7.

$$m=\frac{0±\sqrt{28\times 16}}{2\left(-7\right)}$$

Multiply 28 times 16.

$$m=\frac{0±\sqrt{448}}{2\left(-7\right)}$$

Take the square root of 448.

$$m=\frac{0±8\sqrt{7}}{2\left(-7\right)}$$

Multiply 2 times -7.

$$m=\frac{0±8\sqrt{7}}{-14}$$

Now solve the equation m=\frac{0±8\sqrt{7}}{-14} when ± is plus.

$$m=-\frac{4\sqrt{7}}{7}$$

Now solve the equation m=\frac{0±8\sqrt{7}}{-14} when ± is minus.

$$m=\frac{4\sqrt{7}}{7}$$

The equation is now solved.

$$m=-\frac{4\sqrt{7}}{7} m=\frac{4\sqrt{7}}{7}$$