2p^2+p-51=0

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Solution for 2p^2+p-51=0 equation: 


Simplifying
2p2 + p + -51 = 0

Reorder the terms:
-51 + p + 2p2 = 0

Solving
-51 + p + 2p2 = 0

Solving for variable 'p'.

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

Divide each side by '2'.
-25.5 + 0.5p + p2 = 0

Move the constant term to the right:

Add '25.5' to each side of the equation.
-25.5 + 0.5p + 25.5 + p2 = 0 + 25.5

Reorder the terms:
-25.5 + 25.5 + 0.5p + p2 = 0 + 25.5

Combine like terms: -25.5 + 25.5 = 0.0
0.0 + 0.5p + p2 = 0 + 25.5
0.5p + p2 = 0 + 25.5

Combine like terms: 0 + 25.5 = 25.5
0.5p + p2 = 25.5

The p term is p.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5p + 0.25 + p2 = 25.5 + 0.25

Reorder the terms:
0.25 + 0.5p + p2 = 25.5 + 0.25

Combine like terms: 25.5 + 0.25 = 25.75
0.25 + 0.5p + p2 = 25.75

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 25.75

Calculate the square root of the right side: 5.074445783

Break this problem into two subproblems by setting 
(p + 0.5) equal to 5.074445783 and -5.074445783.


Subproblem 1
p + 0.5 = 5.074445783

Simplifying
p + 0.5 = 5.074445783

Reorder the terms:
0.5 + p = 5.074445783

Solving
0.5 + p = 5.074445783

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = 5.074445783 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 5.074445783 + -0.5
p = 5.074445783 + -0.5

Combine like terms: 5.074445783 + -0.5 = 4.574445783
p = 4.574445783

Simplifying
p = 4.574445783


Subproblem 2
p + 0.5 = -5.074445783

Simplifying
p + 0.5 = -5.074445783

Reorder the terms:
0.5 + p = -5.074445783

Solving
0.5 + p = -5.074445783

Solving for variable 'p'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + p = -5.074445783 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -5.074445783 + -0.5
p = -5.074445783 + -0.5

Combine like terms: -5.074445783 + -0.5 = -5.574445783
p = -5.574445783

Simplifying
p = -5.574445783


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {4.574445783, -5.574445783}

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