Solve -5p^2+4=0

$$- 5 p ^ { 2 } + 4 = 0$$

Solve for p

$$p=\frac{2\sqrt{5}}{5}\approx 0.894427191$$

$$p=-\frac{2\sqrt{5}}{5}\approx -0.894427191$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$-5p^{2}=-4$$

Divide both sides by -5.

$$p^{2}=\frac{-4}{-5}$$

Fraction \frac{-4}{-5} can be simplified to \frac{4}{5} by removing the negative sign from both the numerator and the denominator.

$$p^{2}=\frac{4}{5}$$

Take the square root of both sides of the equation.

$$p=\frac{2\sqrt{5}}{5} p=-\frac{2\sqrt{5}}{5}$$

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.

$$-5p^{2}+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 4}}{2\left(-5\right)}$$

Square 0.

$$p=\frac{0±\sqrt{-4\left(-5\right)\times 4}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$p=\frac{0±\sqrt{20\times 4}}{2\left(-5\right)}$$

Multiply 20 times 4.

$$p=\frac{0±\sqrt{80}}{2\left(-5\right)}$$

Take the square root of 80.

$$p=\frac{0±4\sqrt{5}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$p=\frac{0±4\sqrt{5}}{-10}$$

Now solve the equation p=\frac{0±4\sqrt{5}}{-10} when ± is plus.

$$p=-\frac{2\sqrt{5}}{5}$$

Now solve the equation p=\frac{0±4\sqrt{5}}{-10} when ± is minus.

$$p=\frac{2\sqrt{5}}{5}$$

The equation is now solved.

$$p=-\frac{2\sqrt{5}}{5} p=\frac{2\sqrt{5}}{5}$$