(5p+2)(5p+2)=8

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Solution for (5p+2)(5p+2)=8 equation: 


Simplifying
(5p + 2)(5p + 2) = 8

Reorder the terms:
(2 + 5p)(5p + 2) = 8

Reorder the terms:
(2 + 5p)(2 + 5p) = 8

Multiply (2 + 5p) * (2 + 5p)
(2(2 + 5p) + 5p * (2 + 5p)) = 8
((2 * 2 + 5p * 2) + 5p * (2 + 5p)) = 8
((4 + 10p) + 5p * (2 + 5p)) = 8
(4 + 10p + (2 * 5p + 5p * 5p)) = 8
(4 + 10p + (10p + 25p2)) = 8

Combine like terms: 10p + 10p = 20p
(4 + 20p + 25p2) = 8

Solving
4 + 20p + 25p2 = 8

Solving for variable 'p'.

Reorder the terms:
4 + -8 + 20p + 25p2 = 8 + -8

Combine like terms: 4 + -8 = -4
-4 + 20p + 25p2 = 8 + -8

Combine like terms: 8 + -8 = 0
-4 + 20p + 25p2 = 0

Begin completing the square.  Divide all terms by
25 the coefficient of the squared term: 

Divide each side by '25'.
-0.16 + 0.8p + p2 = 0

Move the constant term to the right:

Add '0.16' to each side of the equation.
-0.16 + 0.8p + 0.16 + p2 = 0 + 0.16

Reorder the terms:
-0.16 + 0.16 + 0.8p + p2 = 0 + 0.16

Combine like terms: -0.16 + 0.16 = 0.00
0.00 + 0.8p + p2 = 0 + 0.16
0.8p + p2 = 0 + 0.16

Combine like terms: 0 + 0.16 = 0.16
0.8p + p2 = 0.16

The p term is 0.8p.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8p + 0.16 + p2 = 0.16 + 0.16

Reorder the terms:
0.16 + 0.8p + p2 = 0.16 + 0.16

Combine like terms: 0.16 + 0.16 = 0.32
0.16 + 0.8p + p2 = 0.32

Factor a perfect square on the left side:
(p + 0.4)(p + 0.4) = 0.32

Calculate the square root of the right side: 0.565685425

Break this problem into two subproblems by setting 
(p + 0.4) equal to 0.565685425 and -0.565685425.


Subproblem 1
p + 0.4 = 0.565685425

Simplifying
p + 0.4 = 0.565685425

Reorder the terms:
0.4 + p = 0.565685425

Solving
0.4 + p = 0.565685425

Solving for variable 'p'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + p = 0.565685425 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + p = 0.565685425 + -0.4
p = 0.565685425 + -0.4

Combine like terms: 0.565685425 + -0.4 = 0.165685425
p = 0.165685425

Simplifying
p = 0.165685425


Subproblem 2
p + 0.4 = -0.565685425

Simplifying
p + 0.4 = -0.565685425

Reorder the terms:
0.4 + p = -0.565685425

Solving
0.4 + p = -0.565685425

Solving for variable 'p'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + p = -0.565685425 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + p = -0.565685425 + -0.4
p = -0.565685425 + -0.4

Combine like terms: -0.565685425 + -0.4 = -0.965685425
p = -0.965685425

Simplifying
p = -0.965685425


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.165685425, -0.965685425}

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