Solve -25+(-16P)(3P)=-942

$$- 25 + ( - 16 P ) ( 3 P ) = - 942$$

Solve for P

$$P = \frac{\sqrt{2751}}{12} \approx 4.370831347$$

$$P = -\frac{\sqrt{2751}}{12} \approx -4.370831347$$

Steps by Finding Square Root

Multiply P and P to get P^{2}.

$$-25-16P^{2}\times 3=-942$$

Multiply -16 and 3 to get -48.

$$-25-48P^{2}=-942$$

Add 25 to both sides.

$$-48P^{2}=-942+25$$

Add -942 and 25 to get -917.

$$-48P^{2}=-917$$

Divide both sides by -48.

$$P^{2}=\frac{-917}{-48}$$

Fraction \frac{-917}{-48} can be simplified to \frac{917}{48} by removing the negative sign from both the numerator and the denominator.

$$P^{2}=\frac{917}{48}$$

Take the square root of both sides of the equation.

$$P=\frac{\sqrt{2751}}{12} P=-\frac{\sqrt{2751}}{12}$$

Steps Using the Quadratic Formula

Multiply P and P to get P^{2}.

$$-25-16P^{2}\times 3=-942$$

Multiply -16 and 3 to get -48.

$$-25-48P^{2}=-942$$

Add 942 to both sides.

$$-25-48P^{2}+942=0$$

Add -25 and 942 to get 917.

$$917-48P^{2}=0$$

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.

$$-48P^{2}+917=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -48 for a, 0 for b, and 917 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$P=\frac{0±\sqrt{0^{2}-4\left(-48\right)\times 917}}{2\left(-48\right)}$$

Square 0.

$$P=\frac{0±\sqrt{-4\left(-48\right)\times 917}}{2\left(-48\right)}$$

Multiply -4 times -48.

$$P=\frac{0±\sqrt{192\times 917}}{2\left(-48\right)}$$

Multiply 192 times 917.

$$P=\frac{0±\sqrt{176064}}{2\left(-48\right)}$$

Take the square root of 176064.

$$P=\frac{0±8\sqrt{2751}}{2\left(-48\right)}$$

Multiply 2 times -48.

$$P=\frac{0±8\sqrt{2751}}{-96}$$

Now solve the equation P=\frac{0±8\sqrt{2751}}{-96} when ± is plus.

$$P=-\frac{\sqrt{2751}}{12}$$

Now solve the equation P=\frac{0±8\sqrt{2751}}{-96} when ± is minus.

$$P=\frac{\sqrt{2751}}{12}$$

The equation is now solved.

$$P=-\frac{\sqrt{2751}}{12} P=\frac{\sqrt{2751}}{12}$$