p^2+4p-71=-10

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Solution for p^2+4p-71=-10 equation: 


Simplifying
p2 + 4p + -71 = -10

Reorder the terms:
-71 + 4p + p2 = -10

Solving
-71 + 4p + p2 = -10

Solving for variable 'p'.

Reorder the terms:
-71 + 10 + 4p + p2 = -10 + 10

Combine like terms: -71 + 10 = -61
-61 + 4p + p2 = -10 + 10

Combine like terms: -10 + 10 = 0
-61 + 4p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '61' to each side of the equation.
-61 + 4p + 61 + p2 = 0 + 61

Reorder the terms:
-61 + 61 + 4p + p2 = 0 + 61

Combine like terms: -61 + 61 = 0
0 + 4p + p2 = 0 + 61
4p + p2 = 0 + 61

Combine like terms: 0 + 61 = 61
4p + p2 = 61

The p term is 4p.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4p + 4 + p2 = 61 + 4

Reorder the terms:
4 + 4p + p2 = 61 + 4

Combine like terms: 61 + 4 = 65
4 + 4p + p2 = 65

Factor a perfect square on the left side:
(p + 2)(p + 2) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(p + 2) equal to 8.062257748 and -8.062257748.


Subproblem 1
p + 2 = 8.062257748

Simplifying
p + 2 = 8.062257748

Reorder the terms:
2 + p = 8.062257748

Solving
2 + p = 8.062257748

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + p = 8.062257748 + -2

Combine like terms: 2 + -2 = 0
0 + p = 8.062257748 + -2
p = 8.062257748 + -2

Combine like terms: 8.062257748 + -2 = 6.062257748
p = 6.062257748

Simplifying
p = 6.062257748


Subproblem 2
p + 2 = -8.062257748

Simplifying
p + 2 = -8.062257748

Reorder the terms:
2 + p = -8.062257748

Solving
2 + p = -8.062257748

Solving for variable 'p'.

Move all terms containing p to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + p = -8.062257748 + -2

Combine like terms: 2 + -2 = 0
0 + p = -8.062257748 + -2
p = -8.062257748 + -2

Combine like terms: -8.062257748 + -2 = -10.062257748
p = -10.062257748

Simplifying
p = -10.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {6.062257748, -10.062257748}

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