Solve 63^2/16p^2+17^2/4p^2=75

$$\frac { 63 ^ { 2 } } { 16 } p ^ { 2 } + \frac { 17 ^ { 2 } } { 4 } p ^ { 2 } = 75$$

Solve for p

$$p=\frac{4\sqrt{615}}{205}\approx 0.483886703$$

$$p=-\frac{4\sqrt{615}}{205}\approx -0.483886703$$

Steps by Finding Square Root

Multiply both sides of the equation by 16, the least common multiple of 16,4.

$$63^{2}p^{2}+4\times 17^{2}p^{2}=1200$$

Calculate 63 to the power of 2 and get 3969.

$$3969p^{2}+4\times 17^{2}p^{2}=1200$$

Calculate 17 to the power of 2 and get 289.

$$3969p^{2}+4\times 289p^{2}=1200$$

Multiply 4 and 289 to get 1156.

$$3969p^{2}+1156p^{2}=1200$$

Combine 3969p^{2} and 1156p^{2} to get 5125p^{2}.

$$5125p^{2}=1200$$

Divide both sides by 5125.

$$p^{2}=\frac{1200}{5125}$$

Reduce the fraction \frac{1200}{5125} to lowest terms by extracting and canceling out 25.

$$p^{2}=\frac{48}{205}$$

Take the square root of both sides of the equation.

$$p=\frac{4\sqrt{615}}{205} p=-\frac{4\sqrt{615}}{205}$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 16, the least common multiple of 16,4.

$$63^{2}p^{2}+4\times 17^{2}p^{2}=1200$$

Calculate 63 to the power of 2 and get 3969.

$$3969p^{2}+4\times 17^{2}p^{2}=1200$$

Calculate 17 to the power of 2 and get 289.

$$3969p^{2}+4\times 289p^{2}=1200$$

Multiply 4 and 289 to get 1156.

$$3969p^{2}+1156p^{2}=1200$$

Combine 3969p^{2} and 1156p^{2} to get 5125p^{2}.

$$5125p^{2}=1200$$

Subtract 1200 from both sides.

$$5125p^{2}-1200=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5125 for a, 0 for b, and -1200 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{0±\sqrt{0^{2}-4\times 5125\left(-1200\right)}}{2\times 5125}$$

Square 0.

$$p=\frac{0±\sqrt{-4\times 5125\left(-1200\right)}}{2\times 5125}$$

Multiply -4 times 5125.

$$p=\frac{0±\sqrt{-20500\left(-1200\right)}}{2\times 5125}$$

Multiply -20500 times -1200.

$$p=\frac{0±\sqrt{24600000}}{2\times 5125}$$

Take the square root of 24600000.

$$p=\frac{0±200\sqrt{615}}{2\times 5125}$$

Multiply 2 times 5125.

$$p=\frac{0±200\sqrt{615}}{10250}$$

Now solve the equation p=\frac{0±200\sqrt{615}}{10250} when ± is plus.

$$p=\frac{4\sqrt{615}}{205}$$

Now solve the equation p=\frac{0±200\sqrt{615}}{10250} when ± is minus.

$$p=-\frac{4\sqrt{615}}{205}$$

The equation is now solved.

$$p=\frac{4\sqrt{615}}{205} p=-\frac{4\sqrt{615}}{205}$$