Solve 120=(10+b^2)6

$$120 = ( 10 + b ^ { 2 } ) 6$$

Solve for b

$$b=\sqrt{10}\approx 3.16227766$$

$$b=-\sqrt{10}\approx -3.16227766$$

Steps by Finding Square Root

Divide both sides by 6.

$$\frac{120}{6}=10+b^{2}$$

Divide 120 by 6 to get 20.

$$20=10+b^{2}$$

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

$$10+b^{2}=20$$

Subtract 10 from both sides.

$$b^{2}=20-10$$

Subtract 10 from 20 to get 10.

$$b^{2}=10$$

Take the square root of both sides of the equation.

$$b=\sqrt{10} b=-\sqrt{10}$$

Steps Using the Quadratic Formula

Divide both sides by 6.

$$\frac{120}{6}=10+b^{2}$$

Divide 120 by 6 to get 20.

$$20=10+b^{2}$$

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

$$10+b^{2}=20$$

Subtract 20 from both sides.

$$10+b^{2}-20=0$$

Subtract 20 from 10 to get -10.

$$-10+b^{2}=0$$

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.

$$b^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\left(-10\right)}}{2}$$

Square 0.

$$b=\frac{0±\sqrt{-4\left(-10\right)}}{2}$$

Multiply -4 times -10.

$$b=\frac{0±\sqrt{40}}{2}$$

Take the square root of 40.

$$b=\frac{0±2\sqrt{10}}{2}$$

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

$$b=\sqrt{10}$$

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

$$b=-\sqrt{10}$$

The equation is now solved.

$$b=\sqrt{10} b=-\sqrt{10}$$