Solve 1-4P^2=-5

$$1 - 4 P ^ { 2 } = - 5$$

Solve for P

$$P = \frac{\sqrt{6}}{2} \approx 1.224744871$$

$$P = -\frac{\sqrt{6}}{2} \approx -1.224744871$$

Steps by Finding Square Root

Subtract 1 from both sides.

$$-4P^{2}=-5-1$$

Subtract 1 from -5 to get -6.

$$-4P^{2}=-6$$

Divide both sides by -4.

$$P^{2}=\frac{-6}{-4}$$

Reduce the fraction \frac{-6}{-4} to lowest terms by extracting and canceling out -2.

$$P^{2}=\frac{3}{2}$$

Take the square root of both sides of the equation.

$$P=\frac{\sqrt{6}}{2} P=-\frac{\sqrt{6}}{2}$$

Steps Using the Quadratic Formula

Add 5 to both sides.

$$1-4P^{2}+5=0$$

Add 1 and 5 to get 6.

$$6-4P^{2}=0$$

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.

$$-4P^{2}+6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$P=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 6}}{2\left(-4\right)}$$

Square 0.

$$P=\frac{0±\sqrt{-4\left(-4\right)\times 6}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$P=\frac{0±\sqrt{16\times 6}}{2\left(-4\right)}$$

Multiply 16 times 6.

$$P=\frac{0±\sqrt{96}}{2\left(-4\right)}$$

Take the square root of 96.

$$P=\frac{0±4\sqrt{6}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$P=\frac{0±4\sqrt{6}}{-8}$$

Now solve the equation P=\frac{0±4\sqrt{6}}{-8} when ± is plus.

$$P=-\frac{\sqrt{6}}{2}$$

Now solve the equation P=\frac{0±4\sqrt{6}}{-8} when ± is minus.

$$P=\frac{\sqrt{6}}{2}$$

The equation is now solved.

$$P=-\frac{\sqrt{6}}{2} P=\frac{\sqrt{6}}{2}$$