p^2-2p-101=-8

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Solution for p^2-2p-101=-8 equation:


Simplifying
p2 + -2p + -101 = -8

Reorder the terms:
-101 + -2p + p2 = -8

Solving
-101 + -2p + p2 = -8

Solving for variable 'p'.

Reorder the terms:
-101 + 8 + -2p + p2 = -8 + 8

Combine like terms: -101 + 8 = -93
-93 + -2p + p2 = -8 + 8

Combine like terms: -8 + 8 = 0
-93 + -2p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + -2p + 93 + p2 = 0 + 93

Reorder the terms:
-93 + 93 + -2p + p2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + -2p + p2 = 0 + 93
-2p + p2 = 0 + 93

Combine like terms: 0 + 93 = 93
-2p + p2 = 93

The p term is -2p.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2p + 1 + p2 = 93 + 1

Reorder the terms:
1 + -2p + p2 = 93 + 1

Combine like terms: 93 + 1 = 94
1 + -2p + p2 = 94

Factor a perfect square on the left side:
(p + -1)(p + -1) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(p + -1) equal to 9.695359715 and -9.695359715.

Subproblem 1

p + -1 = 9.695359715 Simplifying p + -1 = 9.695359715 Reorder the terms: -1 + p = 9.695359715 Solving -1 + p = 9.695359715 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = 9.695359715 + 1 Combine like terms: -1 + 1 = 0 0 + p = 9.695359715 + 1 p = 9.695359715 + 1 Combine like terms: 9.695359715 + 1 = 10.695359715 p = 10.695359715 Simplifying p = 10.695359715

Subproblem 2

p + -1 = -9.695359715 Simplifying p + -1 = -9.695359715 Reorder the terms: -1 + p = -9.695359715 Solving -1 + p = -9.695359715 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + p = -9.695359715 + 1 Combine like terms: -1 + 1 = 0 0 + p = -9.695359715 + 1 p = -9.695359715 + 1 Combine like terms: -9.695359715 + 1 = -8.695359715 p = -8.695359715 Simplifying p = -8.695359715

Solution

The solution to the problem is based on the solutions from the subproblems. p = {10.695359715, -8.695359715}

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