p^2-16p=84

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Solution for p^2-16p=84 equation:


Simplifying
p2 + -16p = 84

Reorder the terms:
-16p + p2 = 84

Solving
-16p + p2 = 84

Solving for variable 'p'.

Reorder the terms:
-84 + -16p + p2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + -16p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -16p + 84 + p2 = 0 + 84

Reorder the terms:
-84 + 84 + -16p + p2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -16p + p2 = 0 + 84
-16p + p2 = 0 + 84

Combine like terms: 0 + 84 = 84
-16p + p2 = 84

The p term is -16p.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16p + 64 + p2 = 84 + 64

Reorder the terms:
64 + -16p + p2 = 84 + 64

Combine like terms: 84 + 64 = 148
64 + -16p + p2 = 148

Factor a perfect square on the left side:
(p + -8)(p + -8) = 148

Calculate the square root of the right side: 12.165525061

Break this problem into two subproblems by setting 
(p + -8) equal to 12.165525061 and -12.165525061.

Subproblem 1

p + -8 = 12.165525061 Simplifying p + -8 = 12.165525061 Reorder the terms: -8 + p = 12.165525061 Solving -8 + p = 12.165525061 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = 12.165525061 + 8 Combine like terms: -8 + 8 = 0 0 + p = 12.165525061 + 8 p = 12.165525061 + 8 Combine like terms: 12.165525061 + 8 = 20.165525061 p = 20.165525061 Simplifying p = 20.165525061

Subproblem 2

p + -8 = -12.165525061 Simplifying p + -8 = -12.165525061 Reorder the terms: -8 + p = -12.165525061 Solving -8 + p = -12.165525061 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + p = -12.165525061 + 8 Combine like terms: -8 + 8 = 0 0 + p = -12.165525061 + 8 p = -12.165525061 + 8 Combine like terms: -12.165525061 + 8 = -4.165525061 p = -4.165525061 Simplifying p = -4.165525061

Solution

The solution to the problem is based on the solutions from the subproblems. p = {20.165525061, -4.165525061}

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