2p^2+9p-7=0

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

Simplifying
2p2 + 9p + -7 = 0

Reorder the terms:
-7 + 9p + 2p2 = 0

Solving
-7 + 9p + 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'.
-3.5 + 4.5p + p2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 4.5p + 3.5 + p2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 4.5p + p2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 4.5p + p2 = 0 + 3.5
4.5p + p2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
4.5p + p2 = 3.5

The p term is 4.5p.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5p + 5.0625 + p2 = 3.5 + 5.0625

Reorder the terms:
5.0625 + 4.5p + p2 = 3.5 + 5.0625

Combine like terms: 3.5 + 5.0625 = 8.5625
5.0625 + 4.5p + p2 = 8.5625

Factor a perfect square on the left side:
(p + 2.25)(p + 2.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(p + 2.25) equal to 2.926174978 and -2.926174978.

Subproblem 1
p + 2.25 = 2.926174978

Simplifying
p + 2.25 = 2.926174978

Reorder the terms:
2.25 + p = 2.926174978

Solving
2.25 + p = 2.926174978

Solving for variable 'p'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + p = 2.926174978 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + p = 2.926174978 + -2.25
p = 2.926174978 + -2.25

Combine like terms: 2.926174978 + -2.25 = 0.676174978
p = 0.676174978

Simplifying
p = 0.676174978

Subproblem 2
p + 2.25 = -2.926174978

Simplifying
p + 2.25 = -2.926174978

Reorder the terms:
2.25 + p = -2.926174978

Solving
2.25 + p = -2.926174978

Solving for variable 'p'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + p = -2.926174978 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + p = -2.926174978 + -2.25
p = -2.926174978 + -2.25

Combine like terms: -2.926174978 + -2.25 = -5.176174978
p = -5.176174978

Simplifying
p = -5.176174978

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.676174978, -5.176174978}