Solve 3b^2-72=0

$$3 b ^ { 2 } - 72 = 0$$

Solve for b

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

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

Steps by Finding Square Root

Add 72 to both sides. Anything plus zero gives itself.

$$3b^{2}=72$$

Divide both sides by 3.

$$b^{2}=\frac{72}{3}$$

Divide 72 by 3 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

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.

$$3b^{2}-72=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -72 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$b=\frac{0±\sqrt{0^{2}-4\times 3\left(-72\right)}}{2\times 3}$$

Square 0.

$$b=\frac{0±\sqrt{-4\times 3\left(-72\right)}}{2\times 3}$$

Multiply -4 times 3.

$$b=\frac{0±\sqrt{-12\left(-72\right)}}{2\times 3}$$

Multiply -12 times -72.

$$b=\frac{0±\sqrt{864}}{2\times 3}$$

Take the square root of 864.

$$b=\frac{0±12\sqrt{6}}{2\times 3}$$

Multiply 2 times 3.

$$b=\frac{0±12\sqrt{6}}{6}$$

Now solve the equation b=\frac{0±12\sqrt{6}}{6} when ± is plus.

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

Now solve the equation b=\frac{0±12\sqrt{6}}{6} when ± is minus.

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

The equation is now solved.

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