8p^2+7p-9=0

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Solution for 8p^2+7p-9=0 equation: 


Simplifying
8p2 + 7p + -9 = 0

Reorder the terms:
-9 + 7p + 8p2 = 0

Solving
-9 + 7p + 8p2 = 0

Solving for variable 'p'.

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

Divide each side by '8'.
-1.125 + 0.875p + p2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 0.875p + 1.125 + p2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 0.875p + p2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 0.875p + p2 = 0 + 1.125
0.875p + p2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
0.875p + p2 = 1.125

The p term is 0.875p.  Take half its coefficient (0.4375).
Square it (0.19140625) and add it to both sides.

Add '0.19140625' to each side of the equation.
0.875p + 0.19140625 + p2 = 1.125 + 0.19140625

Reorder the terms:
0.19140625 + 0.875p + p2 = 1.125 + 0.19140625

Combine like terms: 1.125 + 0.19140625 = 1.31640625
0.19140625 + 0.875p + p2 = 1.31640625

Factor a perfect square on the left side:
(p + 0.4375)(p + 0.4375) = 1.31640625

Calculate the square root of the right side: 1.147347484

Break this problem into two subproblems by setting 
(p + 0.4375) equal to 1.147347484 and -1.147347484.


Subproblem 1
p + 0.4375 = 1.147347484

Simplifying
p + 0.4375 = 1.147347484

Reorder the terms:
0.4375 + p = 1.147347484

Solving
0.4375 + p = 1.147347484

Solving for variable 'p'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + p = 1.147347484 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + p = 1.147347484 + -0.4375
p = 1.147347484 + -0.4375

Combine like terms: 1.147347484 + -0.4375 = 0.709847484
p = 0.709847484

Simplifying
p = 0.709847484


Subproblem 2
p + 0.4375 = -1.147347484

Simplifying
p + 0.4375 = -1.147347484

Reorder the terms:
0.4375 + p = -1.147347484

Solving
0.4375 + p = -1.147347484

Solving for variable 'p'.

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

Add '-0.4375' to each side of the equation.
0.4375 + -0.4375 + p = -1.147347484 + -0.4375

Combine like terms: 0.4375 + -0.4375 = 0.0000
0.0000 + p = -1.147347484 + -0.4375
p = -1.147347484 + -0.4375

Combine like terms: -1.147347484 + -0.4375 = -1.584847484
p = -1.584847484

Simplifying
p = -1.584847484


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.709847484, -1.584847484}

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