Solve 22p^2-50=0

$$22 p ^ { 2 } - 50 = 0$$

Solve for p

$$p = \frac{5 \sqrt{11}}{11} \approx 1.507556723$$

$$p = -\frac{5 \sqrt{11}}{11} \approx -1.507556723$$

Steps by Finding Square Root

Add 50 to both sides. Anything plus zero gives itself.

$$22p^{2}=50$$

Divide both sides by 22.

$$p^{2}=\frac{50}{22}$$

Reduce the fraction \frac{50}{22} to lowest terms by extracting and canceling out 2.

$$p^{2}=\frac{25}{11}$$

Take the square root of both sides of the equation.

$$p=\frac{5\sqrt{11}}{11} p=-\frac{5\sqrt{11}}{11}$$

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.

$$22p^{2}-50=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 22 for a, 0 for b, and -50 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 22\left(-50\right)}}{2\times 22}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 22\left(-50\right)}}{2\times 22}$$

Multiply -4 times 22.

$$p=\frac{0±\sqrt{-88\left(-50\right)}}{2\times 22}$$

Multiply -88 times -50.

$$p=\frac{0±\sqrt{4400}}{2\times 22}$$

Take the square root of 4400.

$$p=\frac{0±20\sqrt{11}}{2\times 22}$$

Multiply 2 times 22.

$$p=\frac{0±20\sqrt{11}}{44}$$

Now solve the equation p=\frac{0±20\sqrt{11}}{44} when ± is plus.

$$p=\frac{5\sqrt{11}}{11}$$

Now solve the equation p=\frac{0±20\sqrt{11}}{44} when ± is minus.

$$p=-\frac{5\sqrt{11}}{11}$$

The equation is now solved.

$$p=\frac{5\sqrt{11}}{11} p=-\frac{5\sqrt{11}}{11}$$