p^2+8p+10=0

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Solution for p^2+8p+10=0 equation: 


Simplifying
p2 + 8p + 10 = 0

Reorder the terms:
10 + 8p + p2 = 0

Solving
10 + 8p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 8p + -10 + p2 = 0 + -10

Reorder the terms:
10 + -10 + 8p + p2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 8p + p2 = 0 + -10
8p + p2 = 0 + -10

Combine like terms: 0 + -10 = -10
8p + p2 = -10

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 = -10 + 16

Reorder the terms:
16 + 8p + p2 = -10 + 16

Combine like terms: -10 + 16 = 6
16 + 8p + p2 = 6

Factor a perfect square on the left side:
(p + 4)(p + 4) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(p + 4) equal to 2.449489743 and -2.449489743.


Subproblem 1
p + 4 = 2.449489743

Simplifying
p + 4 = 2.449489743

Reorder the terms:
4 + p = 2.449489743

Solving
4 + p = 2.449489743

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 = 2.449489743 + -4

Combine like terms: 4 + -4 = 0
0 + p = 2.449489743 + -4
p = 2.449489743 + -4

Combine like terms: 2.449489743 + -4 = -1.550510257
p = -1.550510257

Simplifying
p = -1.550510257


Subproblem 2
p + 4 = -2.449489743

Simplifying
p + 4 = -2.449489743

Reorder the terms:
4 + p = -2.449489743

Solving
4 + p = -2.449489743

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 = -2.449489743 + -4

Combine like terms: 4 + -4 = 0
0 + p = -2.449489743 + -4
p = -2.449489743 + -4

Combine like terms: -2.449489743 + -4 = -6.449489743
p = -6.449489743

Simplifying
p = -6.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {-1.550510257, -6.449489743}

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