2p^2+10p-4=0

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Solution for 2p^2+10p-4=0 equation: 


Simplifying
2p2 + 10p + -4 = 0

Reorder the terms:
-4 + 10p + 2p2 = 0

Solving
-4 + 10p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + 5p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-2 + 5p + p2)' equal to zero and attempt to solve:

Simplifying
-2 + 5p + p2 = 0

Solving
-2 + 5p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 5p + 2 + p2 = 0 + 2

Reorder the terms:
-2 + 2 + 5p + p2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 5p + p2 = 0 + 2
5p + p2 = 0 + 2

Combine like terms: 0 + 2 = 2
5p + p2 = 2

The p term is 5p.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5p + 6.25 + p2 = 2 + 6.25

Reorder the terms:
6.25 + 5p + p2 = 2 + 6.25

Combine like terms: 2 + 6.25 = 8.25
6.25 + 5p + p2 = 8.25

Factor a perfect square on the left side:
(p + 2.5)(p + 2.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(p + 2.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
p + 2.5 = 2.872281323

Simplifying
p + 2.5 = 2.872281323

Reorder the terms:
2.5 + p = 2.872281323

Solving
2.5 + p = 2.872281323

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = 2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = 2.872281323 + -2.5
p = 2.872281323 + -2.5

Combine like terms: 2.872281323 + -2.5 = 0.372281323
p = 0.372281323

Simplifying
p = 0.372281323


Subproblem 2
p + 2.5 = -2.872281323

Simplifying
p + 2.5 = -2.872281323

Reorder the terms:
2.5 + p = -2.872281323

Solving
2.5 + p = -2.872281323

Solving for variable 'p'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + p = -2.872281323 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + p = -2.872281323 + -2.5
p = -2.872281323 + -2.5

Combine like terms: -2.872281323 + -2.5 = -5.372281323
p = -5.372281323

Simplifying
p = -5.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.372281323, -5.372281323}
Solution
p = {0.372281323, -5.372281323}

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