6p^2+10p-13=0

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Solution for 6p^2+10p-13=0 equation: 


Simplifying
6p2 + 10p + -13 = 0

Reorder the terms:
-13 + 10p + 6p2 = 0

Solving
-13 + 10p + 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'.
-2.166666667 + 1.666666667p + p2 = 0

Move the constant term to the right:

Add '2.166666667' to each side of the equation.
-2.166666667 + 1.666666667p + 2.166666667 + p2 = 0 + 2.166666667

Reorder the terms:
-2.166666667 + 2.166666667 + 1.666666667p + p2 = 0 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + 1.666666667p + p2 = 0 + 2.166666667
1.666666667p + p2 = 0 + 2.166666667

Combine like terms: 0 + 2.166666667 = 2.166666667
1.666666667p + p2 = 2.166666667

The p term is 1.666666667p.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667p + 0.6944444447 + p2 = 2.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667p + p2 = 2.166666667 + 0.6944444447

Combine like terms: 2.166666667 + 0.6944444447 = 2.8611111117
0.6944444447 + 1.666666667p + p2 = 2.8611111117

Factor a perfect square on the left side:
(p + 0.8333333335)(p + 0.8333333335) = 2.8611111117

Calculate the square root of the right side: 1.691481928

Break this problem into two subproblems by setting 
(p + 0.8333333335) equal to 1.691481928 and -1.691481928.


Subproblem 1
p + 0.8333333335 = 1.691481928

Simplifying
p + 0.8333333335 = 1.691481928

Reorder the terms:
0.8333333335 + p = 1.691481928

Solving
0.8333333335 + p = 1.691481928

Solving for variable 'p'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + p = 1.691481928 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + p = 1.691481928 + -0.8333333335
p = 1.691481928 + -0.8333333335

Combine like terms: 1.691481928 + -0.8333333335 = 0.8581485945
p = 0.8581485945

Simplifying
p = 0.8581485945


Subproblem 2
p + 0.8333333335 = -1.691481928

Simplifying
p + 0.8333333335 = -1.691481928

Reorder the terms:
0.8333333335 + p = -1.691481928

Solving
0.8333333335 + p = -1.691481928

Solving for variable 'p'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + p = -1.691481928 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + p = -1.691481928 + -0.8333333335
p = -1.691481928 + -0.8333333335

Combine like terms: -1.691481928 + -0.8333333335 = -2.5248152615
p = -2.5248152615

Simplifying
p = -2.5248152615


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.8581485945, -2.5248152615}

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