Solve 5b^2-126-65=0

$$5 b ^ { 2 } - 126 - 65 = 0$$

Solve for b

$$b = \frac{\sqrt{955}}{5} \approx 6.180614856$$

$$b = -\frac{\sqrt{955}}{5} \approx -6.180614856$$

Steps by Finding Square Root

Subtract 65 from -126 to get -191.

$$5b^{2}-191=0$$

Add 191 to both sides. Anything plus zero gives itself.

$$5b^{2}=191$$

Divide both sides by 5.

$$b^{2}=\frac{191}{5}$$

Take the square root of both sides of the equation.

$$b=\frac{\sqrt{955}}{5} b=-\frac{\sqrt{955}}{5}$$

Steps Using the Quadratic Formula

Subtract 65 from -126 to get -191.

$$5b^{2}-191=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -191 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 5\left(-191\right)}}{2\times 5}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 5\left(-191\right)}}{2\times 5}$$

Multiply -4 times 5.

$$b=\frac{0±\sqrt{-20\left(-191\right)}}{2\times 5}$$

Multiply -20 times -191.

$$b=\frac{0±\sqrt{3820}}{2\times 5}$$

Take the square root of 3820.

$$b=\frac{0±2\sqrt{955}}{2\times 5}$$

Multiply 2 times 5.

$$b=\frac{0±2\sqrt{955}}{10}$$

Now solve the equation b=\frac{0±2\sqrt{955}}{10} when ± is plus.

$$b=\frac{\sqrt{955}}{5}$$

Now solve the equation b=\frac{0±2\sqrt{955}}{10} when ± is minus.

$$b=-\frac{\sqrt{955}}{5}$$

The equation is now solved.

$$b=\frac{\sqrt{955}}{5} b=-\frac{\sqrt{955}}{5}$$