6p^2+p-25=0

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Solution for 6p^2+p-25=0 equation: 


Simplifying
6p2 + p + -25 = 0

Reorder the terms:
-25 + p + 6p2 = 0

Solving
-25 + p + 6p2 = 0

Solving for variable 'p'.

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

Divide each side by '6'.
-4.166666667 + 0.1666666667p + p2 = 0

Move the constant term to the right:

Add '4.166666667' to each side of the equation.
-4.166666667 + 0.1666666667p + 4.166666667 + p2 = 0 + 4.166666667

Reorder the terms:
-4.166666667 + 4.166666667 + 0.1666666667p + p2 = 0 + 4.166666667

Combine like terms: -4.166666667 + 4.166666667 = 0.000000000
0.000000000 + 0.1666666667p + p2 = 0 + 4.166666667
0.1666666667p + p2 = 0 + 4.166666667

Combine like terms: 0 + 4.166666667 = 4.166666667
0.1666666667p + p2 = 4.166666667

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.
0.1666666667p + 0.25 + p2 = 4.166666667 + 0.25

Reorder the terms:
0.25 + 0.1666666667p + p2 = 4.166666667 + 0.25

Combine like terms: 4.166666667 + 0.25 = 4.416666667
0.25 + 0.1666666667p + p2 = 4.416666667

Factor a perfect square on the left side:
(p + 0.5)(p + 0.5) = 4.416666667

Calculate the square root of the right side: 2.101586702

Break this problem into two subproblems by setting 
(p + 0.5) equal to 2.101586702 and -2.101586702.


Subproblem 1
p + 0.5 = 2.101586702

Simplifying
p + 0.5 = 2.101586702

Reorder the terms:
0.5 + p = 2.101586702

Solving
0.5 + p = 2.101586702

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 = 2.101586702 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = 2.101586702 + -0.5
p = 2.101586702 + -0.5

Combine like terms: 2.101586702 + -0.5 = 1.601586702
p = 1.601586702

Simplifying
p = 1.601586702


Subproblem 2
p + 0.5 = -2.101586702

Simplifying
p + 0.5 = -2.101586702

Reorder the terms:
0.5 + p = -2.101586702

Solving
0.5 + p = -2.101586702

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 = -2.101586702 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + p = -2.101586702 + -0.5
p = -2.101586702 + -0.5

Combine like terms: -2.101586702 + -0.5 = -2.601586702
p = -2.601586702

Simplifying
p = -2.601586702


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {1.601586702, -2.601586702}

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