Solve b^2+4-5=1/6

$$b ^ { 2 } + 4 - 5 = \frac { 1 } { 6 }$$

Solve for b

$$b = \frac{\sqrt{42}}{6} \approx 1.08012345$$

$$b = -\frac{\sqrt{42}}{6} \approx -1.08012345$$

Steps by Finding Square Root

Subtract 5 from 4 to get -1.

$$b^{2}-1=\frac{1}{6}$$

Add 1 to both sides.

$$b^{2}=\frac{1}{6}+1$$

Add \frac{1}{6} and 1 to get \frac{7}{6}.

$$b^{2}=\frac{7}{6}$$

Take the square root of both sides of the equation.

$$b=\frac{\sqrt{42}}{6} b=-\frac{\sqrt{42}}{6}$$

Steps Using the Quadratic Formula

Subtract 5 from 4 to get -1.

$$b^{2}-1=\frac{1}{6}$$

Subtract \frac{1}{6} from both sides.

$$b^{2}-1-\frac{1}{6}=0$$

Subtract \frac{1}{6} from -1 to get -\frac{7}{6}.

$$b^{2}-\frac{7}{6}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{7}{6} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-\frac{7}{6}\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-\frac{7}{6}\right)}}{2}$$

Multiply -4 times -\frac{7}{6}.

$$b=\frac{0±\sqrt{\frac{14}{3}}}{2}$$

Take the square root of \frac{14}{3}.

$$b=\frac{0±\frac{\sqrt{42}}{3}}{2}$$

Now solve the equation b=\frac{0±\frac{\sqrt{42}}{3}}{2} when ± is plus.

$$b=\frac{\sqrt{42}}{6}$$

Now solve the equation b=\frac{0±\frac{\sqrt{42}}{3}}{2} when ± is minus.

$$b=-\frac{\sqrt{42}}{6}$$

The equation is now solved.

$$b=\frac{\sqrt{42}}{6} b=-\frac{\sqrt{42}}{6}$$