p^2+6p=6

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Solution for p^2+6p=6 equation:


Simplifying
p2 + 6p = 6

Reorder the terms:
6p + p2 = 6

Solving
6p + p2 = 6

Solving for variable 'p'.

Reorder the terms:
-6 + 6p + p2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 6p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 6p + 6 + p2 = 0 + 6

Reorder the terms:
-6 + 6 + 6p + p2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 6p + p2 = 0 + 6
6p + p2 = 0 + 6

Combine like terms: 0 + 6 = 6
6p + p2 = 6

The p term is 6p.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6p + 9 + p2 = 6 + 9

Reorder the terms:
9 + 6p + p2 = 6 + 9

Combine like terms: 6 + 9 = 15
9 + 6p + p2 = 15

Factor a perfect square on the left side:
(p + 3)(p + 3) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(p + 3) equal to 3.872983346 and -3.872983346.

Subproblem 1

p + 3 = 3.872983346 Simplifying p + 3 = 3.872983346 Reorder the terms: 3 + p = 3.872983346 Solving 3 + p = 3.872983346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = 3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + p = 3.872983346 + -3 p = 3.872983346 + -3 Combine like terms: 3.872983346 + -3 = 0.872983346 p = 0.872983346 Simplifying p = 0.872983346

Subproblem 2

p + 3 = -3.872983346 Simplifying p + 3 = -3.872983346 Reorder the terms: 3 + p = -3.872983346 Solving 3 + p = -3.872983346 Solving for variable 'p'. Move all terms containing p to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + p = -3.872983346 + -3 Combine like terms: 3 + -3 = 0 0 + p = -3.872983346 + -3 p = -3.872983346 + -3 Combine like terms: -3.872983346 + -3 = -6.872983346 p = -6.872983346 Simplifying p = -6.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. p = {0.872983346, -6.872983346}

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