Solve 3-m^2=-7

$$3 - m ^ { 2 } = - 7$$

Solve for m

$$m=\sqrt{10}\approx 3.16227766$$

$$m=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Subtract 3 from both sides.

$$-m^{2}=-7-3$$

Subtract 3 from -7 to get -10.

$$-m^{2}=-10$$

Divide both sides by -1.

$$m^{2}=\frac{-10}{-1}$$

Fraction \frac{-10}{-1} can be simplified to 10 by removing the negative sign from both the numerator and the denominator.

$$m^{2}=10$$

Take the square root of both sides of the equation.

$$m=\sqrt{10} m=-\sqrt{10}$$

Steps Using the Quadratic Formula

Add 7 to both sides.

$$3-m^{2}+7=0$$

Add 3 and 7 to get 10.

$$10-m^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-m^{2}+10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-1\right)\times 10}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$m=\frac{0±\sqrt{4\times 10}}{2\left(-1\right)}$$

Multiply 4 times 10.

$$m=\frac{0±\sqrt{40}}{2\left(-1\right)}$$

Take the square root of 40.

$$m=\frac{0±2\sqrt{10}}{2\left(-1\right)}$$

Multiply 2 times -1.

$$m=\frac{0±2\sqrt{10}}{-2}$$

Now solve the equation m=\frac{0±2\sqrt{10}}{-2} when ± is plus.

$$m=-\sqrt{10}$$

Now solve the equation m=\frac{0±2\sqrt{10}}{-2} when ± is minus.

$$m=\sqrt{10}$$

The equation is now solved.

$$m=-\sqrt{10} m=\sqrt{10}$$