Solve 4-13m^2=-46

$$4 - 13 m ^ { 2 } = - 46$$

Solve for m

$$m = \frac{5 \sqrt{26}}{13} \approx 1.961161351$$

$$m = -\frac{5 \sqrt{26}}{13} \approx -1.961161351$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$-13m^{2}=-46-4$$

Subtract 4 from -46 to get -50.

$$-13m^{2}=-50$$

Divide both sides by -13.

$$m^{2}=\frac{-50}{-13}$$

Fraction \frac{-50}{-13} can be simplified to \frac{50}{13} by removing the negative sign from both the numerator and the denominator.

$$m^{2}=\frac{50}{13}$$

Take the square root of both sides of the equation.

$$m=\frac{5\sqrt{26}}{13} m=-\frac{5\sqrt{26}}{13}$$

Steps Using the Quadratic Formula

Add 46 to both sides.

$$4-13m^{2}+46=0$$

Add 4 and 46 to get 50.

$$50-13m^{2}=0$$

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.

$$-13m^{2}+50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -13 for a, 0 for b, and 50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\left(-13\right)\times 50}}{2\left(-13\right)}$$

Square 0.

$$m=\frac{0±\sqrt{-4\left(-13\right)\times 50}}{2\left(-13\right)}$$

Multiply -4 times -13.

$$m=\frac{0±\sqrt{52\times 50}}{2\left(-13\right)}$$

Multiply 52 times 50.

$$m=\frac{0±\sqrt{2600}}{2\left(-13\right)}$$

Take the square root of 2600.

$$m=\frac{0±10\sqrt{26}}{2\left(-13\right)}$$

Multiply 2 times -13.

$$m=\frac{0±10\sqrt{26}}{-26}$$

Now solve the equation m=\frac{0±10\sqrt{26}}{-26} when ± is plus.

$$m=-\frac{5\sqrt{26}}{13}$$

Now solve the equation m=\frac{0±10\sqrt{26}}{-26} when ± is minus.

$$m=\frac{5\sqrt{26}}{13}$$

The equation is now solved.

$$m=-\frac{5\sqrt{26}}{13} m=\frac{5\sqrt{26}}{13}$$