Solve 64g^2-969+36=0

$$64 g ^ { 2 } - 969 + 36 = 0$$

Solve for g

$$g = \frac{\sqrt{933}}{8} \approx 3.818131087$$

$$g = -\frac{\sqrt{933}}{8} \approx -3.818131087$$

Steps by Finding Square Root

Add -969 and 36 to get -933.

$$64g^{2}-933=0$$

Add 933 to both sides. Anything plus zero gives itself.

$$64g^{2}=933$$

Divide both sides by 64.

$$g^{2}=\frac{933}{64}$$

Take the square root of both sides of the equation.

$$g=\frac{\sqrt{933}}{8} g=-\frac{\sqrt{933}}{8}$$

Steps Using the Quadratic Formula

Add -969 and 36 to get -933.

$$64g^{2}-933=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 64 for a, 0 for b, and -933 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$g=\frac{0±\sqrt{0^{2}-4\times 64\left(-933\right)}}{2\times 64}$$

Square 0.

$$g=\frac{0±\sqrt{-4\times 64\left(-933\right)}}{2\times 64}$$

Multiply -4 times 64.

$$g=\frac{0±\sqrt{-256\left(-933\right)}}{2\times 64}$$

Multiply -256 times -933.

$$g=\frac{0±\sqrt{238848}}{2\times 64}$$

Take the square root of 238848.

$$g=\frac{0±16\sqrt{933}}{2\times 64}$$

Multiply 2 times 64.

$$g=\frac{0±16\sqrt{933}}{128}$$

Now solve the equation g=\frac{0±16\sqrt{933}}{128} when ± is plus.

$$g=\frac{\sqrt{933}}{8}$$

Now solve the equation g=\frac{0±16\sqrt{933}}{128} when ± is minus.

$$g=-\frac{\sqrt{933}}{8}$$

The equation is now solved.

$$g=\frac{\sqrt{933}}{8} g=-\frac{\sqrt{933}}{8}$$