Solve for p

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p^{2}=\frac{49}{9}
Divide both sides by 9.
p^{2}-\frac{49}{9}=0
Subtract \frac{49}{9} from both sides.
9p^{2}-49=0
Multiply both sides by 9.
\left(3p-7\right)\left(3p+7\right)=0
Consider 9p^{2}-49. Rewrite 9p^{2}-49 as \left(3p\right)^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
p=\frac{7}{3} p=-\frac{7}{3}
To find equation solutions, solve 3p-7=0 and 3p+7=0.
p^{2}=\frac{49}{9}
Divide both sides by 9.
p=\frac{7}{3} p=-\frac{7}{3}
Take the square root of both sides of the equation.
p^{2}=\frac{49}{9}
Divide both sides by 9.
p^{2}-\frac{49}{9}=0
Subtract \frac{49}{9} from both sides.
p=\frac{0±\sqrt{0^{2}-4\left(-\frac{49}{9}\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{49}{9} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
p=\frac{0±\sqrt{-4\left(-\frac{49}{9}\right)}}{2}
Square 0.
p=\frac{0±\sqrt{\frac{196}{9}}}{2}
Multiply -4 times -\frac{49}{9}.
p=\frac{0±\frac{14}{3}}{2}
Take the square root of \frac{196}{9}.
p=\frac{7}{3}
Now solve the equation p=\frac{0±\frac{14}{3}}{2} when ± is plus.
p=-\frac{7}{3}
Now solve the equation p=\frac{0±\frac{14}{3}}{2} when ± is minus.
p=\frac{7}{3} p=-\frac{7}{3}
The equation is now solved.