Solve (sqrt{36}-1)^2=b^2+1

$$( \sqrt { 36 } - 1 ) ^ { 2 } = b ^ { 2 } + 1$$

Solve for b

$$b=2\sqrt{6}\approx 4.898979486$$

$$b=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Calculate the square root of 36 and get 6.

$$\left(6-1\right)^{2}=b^{2}+1$$

Subtract 1 from 6 to get 5.

$$5^{2}=b^{2}+1$$

Calculate 5 to the power of 2 and get 25.

$$25=b^{2}+1$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}+1=25$$

Subtract 1 from both sides.

$$b^{2}=25-1$$

Subtract 1 from 25 to get 24.

$$b^{2}=24$$

Take the square root of both sides of the equation.

$$b=2\sqrt{6} b=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Calculate the square root of 36 and get 6.

$$\left(6-1\right)^{2}=b^{2}+1$$

Subtract 1 from 6 to get 5.

$$5^{2}=b^{2}+1$$

Calculate 5 to the power of 2 and get 25.

$$25=b^{2}+1$$

Swap sides so that all variable terms are on the left hand side.

$$b^{2}+1=25$$

Subtract 25 from both sides.

$$b^{2}+1-25=0$$

Subtract 25 from 1 to get -24.

$$b^{2}-24=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -24 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-24\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-24\right)}}{2}$$

Multiply -4 times -24.

$$b=\frac{0±\sqrt{96}}{2}$$

Take the square root of 96.

$$b=\frac{0±4\sqrt{6}}{2}$$

Now solve the equation b=\frac{0±4\sqrt{6}}{2} when ± is plus.

$$b=2\sqrt{6}$$

Now solve the equation b=\frac{0±4\sqrt{6}}{2} when ± is minus.

$$b=-2\sqrt{6}$$

The equation is now solved.

$$b=2\sqrt{6} b=-2\sqrt{6}$$