2p^2+18p-14=0

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Solution for 2p^2+18p-14=0 equation: 


Simplifying
2p2 + 18p + -14 = 0

Reorder the terms:
-14 + 18p + 2p2 = 0

Solving
-14 + 18p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 9p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + 9p + p2)' equal to zero and attempt to solve:

Simplifying
-7 + 9p + p2 = 0

Solving
-7 + 9p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 9p + 7 + p2 = 0 + 7

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

Combine like terms: -7 + 7 = 0
0 + 9p + p2 = 0 + 7
9p + p2 = 0 + 7

Combine like terms: 0 + 7 = 7
9p + p2 = 7

The p term is 9p.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9p + 20.25 + p2 = 7 + 20.25

Reorder the terms:
20.25 + 9p + p2 = 7 + 20.25

Combine like terms: 7 + 20.25 = 27.25
20.25 + 9p + p2 = 27.25

Factor a perfect square on the left side:
(p + 4.5)(p + 4.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(p + 4.5) equal to 5.220153254 and -5.220153254.


Subproblem 1
p + 4.5 = 5.220153254

Simplifying
p + 4.5 = 5.220153254

Reorder the terms:
4.5 + p = 5.220153254

Solving
4.5 + p = 5.220153254

Solving for variable 'p'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + p = 5.220153254 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = 5.220153254 + -4.5
p = 5.220153254 + -4.5

Combine like terms: 5.220153254 + -4.5 = 0.720153254
p = 0.720153254

Simplifying
p = 0.720153254


Subproblem 2
p + 4.5 = -5.220153254

Simplifying
p + 4.5 = -5.220153254

Reorder the terms:
4.5 + p = -5.220153254

Solving
4.5 + p = -5.220153254

Solving for variable 'p'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + p = -5.220153254 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = -5.220153254 + -4.5
p = -5.220153254 + -4.5

Combine like terms: -5.220153254 + -4.5 = -9.720153254
p = -9.720153254

Simplifying
p = -9.720153254


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.720153254, -9.720153254}
Solution
p = {0.720153254, -9.720153254}

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