Solve 144q^2=25

$$144 q ^ { 2 } = 25$$

Solve for q

$$q=\frac{5}{12}\approx 0.416666667$$

$$q=-\frac{5}{12}\approx -0.416666667$$

Steps Using Difference of Squares

Divide both sides by 144.

$$q^{2}=\frac{25}{144}$$

Subtract \frac{25}{144} from both sides.

$$q^{2}-\frac{25}{144}=0$$

Multiply both sides by 144.

$$144q^{2}-25=0$$

Consider 144q^{2}-25. Rewrite 144q^{2}-25 as \left(12q\right)^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(12q-5\right)\left(12q+5\right)=0$$

To find equation solutions, solve 12q-5=0 and 12q+5=0.

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Steps by Finding Square Root

Divide both sides by 144.

$$q^{2}=\frac{25}{144}$$

Take the square root of both sides of the equation.

$$q=\frac{5}{12} q=-\frac{5}{12}$$

Steps Using the Quadratic Formula

Divide both sides by 144.

$$q^{2}=\frac{25}{144}$$

Subtract \frac{25}{144} from both sides.

$$q^{2}-\frac{25}{144}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{25}{144} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$q=\frac{0±\sqrt{0^{2}-4\left(-\frac{25}{144}\right)}}{2}$$

Square 0.

$$q=\frac{0±\sqrt{-4\left(-\frac{25}{144}\right)}}{2}$$

Multiply -4 times -\frac{25}{144}.

$$q=\frac{0±\sqrt{\frac{25}{36}}}{2}$$

Take the square root of \frac{25}{36}.

$$q=\frac{0±\frac{5}{6}}{2}$$

Now solve the equation q=\frac{0±\frac{5}{6}}{2} when ± is plus.

$$q=\frac{5}{12}$$

Now solve the equation q=\frac{0±\frac{5}{6}}{2} when ± is minus.

$$q=-\frac{5}{12}$$

The equation is now solved.

$$q=\frac{5}{12} q=-\frac{5}{12}$$