Solve for p
p=6
p=-6
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p^{2}=\frac{252}{7}
Divide both sides by 7.
p^{2}=36
Divide 252 by 7 to get 36.
p^{2}-36=0
Subtract 36 from both sides.
\left(p-6\right)\left(p+6\right)=0
Consider p^{2}-36. Rewrite p^{2}-36 as p^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
p=6 p=-6
To find equation solutions, solve p-6=0 and p+6=0.
p^{2}=\frac{252}{7}
Divide both sides by 7.
p^{2}=36
Divide 252 by 7 to get 36.
p=6 p=-6
Take the square root of both sides of the equation.
p^{2}=\frac{252}{7}
Divide both sides by 7.
p^{2}=36
Divide 252 by 7 to get 36.
p^{2}-36=0
Subtract 36 from both sides.
p=\frac{0±\sqrt{0^{2}-4\left(-36\right)}}{2}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
p=\frac{0±\sqrt{-4\left(-36\right)}}{2}
Square 0.
p=\frac{0±\sqrt{144}}{2}
Multiply -4 times -36.
p=\frac{0±12}{2}
Take the square root of 144.
p=6
Now solve the equation p=\frac{0±12}{2} when ± is plus. Divide 12 by 2.
p=-6
Now solve the equation p=\frac{0±12}{2} when ± is minus. Divide -12 by 2.
p=6 p=-6
The equation is now solved.
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