p*p-8p-63=9

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Solution for p*p-8p-63=9 equation:


Simplifying
p * p + -8p + -63 = 9

Multiply p * p
p2 + -8p + -63 = 9

Reorder the terms:
-63 + -8p + p2 = 9

Solving
-63 + -8p + p2 = 9

Solving for variable 'p'.

Reorder the terms:
-63 + -9 + -8p + p2 = 9 + -9

Combine like terms: -63 + -9 = -72
-72 + -8p + p2 = 9 + -9

Combine like terms: 9 + -9 = 0
-72 + -8p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -8p + 72 + p2 = 0 + 72

Reorder the terms:
-72 + 72 + -8p + p2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -8p + p2 = 0 + 72
-8p + p2 = 0 + 72

Combine like terms: 0 + 72 = 72
-8p + p2 = 72

The p term is -8p.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8p + 16 + p2 = 72 + 16

Reorder the terms:
16 + -8p + p2 = 72 + 16

Combine like terms: 72 + 16 = 88
16 + -8p + p2 = 88

Factor a perfect square on the left side:
(p + -4)(p + -4) = 88

Calculate the square root of the right side: 9.38083152

Break this problem into two subproblems by setting 
(p + -4) equal to 9.38083152 and -9.38083152.

Subproblem 1

p + -4 = 9.38083152 Simplifying p + -4 = 9.38083152 Reorder the terms: -4 + p = 9.38083152 Solving -4 + p = 9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = 9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + p = 9.38083152 + 4 p = 9.38083152 + 4 Combine like terms: 9.38083152 + 4 = 13.38083152 p = 13.38083152 Simplifying p = 13.38083152

Subproblem 2

p + -4 = -9.38083152 Simplifying p + -4 = -9.38083152 Reorder the terms: -4 + p = -9.38083152 Solving -4 + p = -9.38083152 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + p = -9.38083152 + 4 Combine like terms: -4 + 4 = 0 0 + p = -9.38083152 + 4 p = -9.38083152 + 4 Combine like terms: -9.38083152 + 4 = -5.38083152 p = -5.38083152 Simplifying p = -5.38083152

Solution

The solution to the problem is based on the solutions from the subproblems. p = {13.38083152, -5.38083152}

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