Solve 1024m^2-91=0

$$1024 m ^ { 2 } - 91 = 0$$

Solve for m

$$m=\frac{\sqrt{91}}{32}\approx 0.298106$$

$$m=-\frac{\sqrt{91}}{32}\approx -0.298106$$

Steps by Finding Square Root

Add 91 to both sides. Anything plus zero gives itself.

$$1024m^{2}=91$$

Divide both sides by 1024.

$$m^{2}=\frac{91}{1024}$$

Take the square root of both sides of the equation.

$$m=\frac{\sqrt{91}}{32} m=-\frac{\sqrt{91}}{32}$$

Steps Using the Quadratic Formula

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.

$$1024m^{2}-91=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1024 for a, 0 for b, and -91 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{0±\sqrt{0^{2}-4\times 1024\left(-91\right)}}{2\times 1024}$$

Square 0.

$$m=\frac{0±\sqrt{-4\times 1024\left(-91\right)}}{2\times 1024}$$

Multiply -4 times 1024.

$$m=\frac{0±\sqrt{-4096\left(-91\right)}}{2\times 1024}$$

Multiply -4096 times -91.

$$m=\frac{0±\sqrt{372736}}{2\times 1024}$$

Take the square root of 372736.

$$m=\frac{0±64\sqrt{91}}{2\times 1024}$$

Multiply 2 times 1024.

$$m=\frac{0±64\sqrt{91}}{2048}$$

Now solve the equation m=\frac{0±64\sqrt{91}}{2048} when ± is plus.

$$m=\frac{\sqrt{91}}{32}$$

Now solve the equation m=\frac{0±64\sqrt{91}}{2048} when ± is minus.

$$m=-\frac{\sqrt{91}}{32}$$

The equation is now solved.

$$m=\frac{\sqrt{91}}{32} m=-\frac{\sqrt{91}}{32}$$