Solve A^2*6=87

$$A ^ { 2 } \times 6 = 87$$

Solve for A

$$A = \frac{\sqrt{58}}{2} \approx 3.807886553$$

$$A = -\frac{\sqrt{58}}{2} \approx -3.807886553$$

Steps by Finding Square Root

Divide both sides by 6.

$$A^{2}=\frac{87}{6}$$

Reduce the fraction \frac{87}{6} to lowest terms by extracting and canceling out 3.

$$A^{2}=\frac{29}{2}$$

Take the square root of both sides of the equation.

$$A=\frac{\sqrt{58}}{2} A=-\frac{\sqrt{58}}{2}$$

Steps Using the Quadratic Formula

Divide both sides by 6.

$$A^{2}=\frac{87}{6}$$

Reduce the fraction \frac{87}{6} to lowest terms by extracting and canceling out 3.

$$A^{2}=\frac{29}{2}$$

Subtract \frac{29}{2} from both sides.

$$A^{2}-\frac{29}{2}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{29}{2} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$A=\frac{0±\sqrt{0^{2}-4\left(-\frac{29}{2}\right)}}{2}$$

Square 0.

$$A=\frac{0±\sqrt{-4\left(-\frac{29}{2}\right)}}{2}$$

Multiply -4 times -\frac{29}{2}.

$$A=\frac{0±\sqrt{58}}{2}$$

Now solve the equation A=\frac{0±\sqrt{58}}{2} when ± is plus.

$$A=\frac{\sqrt{58}}{2}$$

Now solve the equation A=\frac{0±\sqrt{58}}{2} when ± is minus.

$$A=-\frac{\sqrt{58}}{2}$$

The equation is now solved.

$$A=\frac{\sqrt{58}}{2} A=-\frac{\sqrt{58}}{2}$$