2p^2+18p-10=0

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Solution for 2p^2+18p-10=0 equation: 


Simplifying
2p2 + 18p + -10 = 0

Reorder the terms:
-10 + 18p + 2p2 = 0

Solving
-10 + 18p + 2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 9p + p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 9p + p2)' equal to zero and attempt to solve:

Simplifying
-5 + 9p + p2 = 0

Solving
-5 + 9p + p2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 9p + 5 + p2 = 0 + 5

Reorder the terms:
-5 + 5 + 9p + p2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 9p + p2 = 0 + 5
9p + p2 = 0 + 5

Combine like terms: 0 + 5 = 5
9p + p2 = 5

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 = 5 + 20.25

Reorder the terms:
20.25 + 9p + p2 = 5 + 20.25

Combine like terms: 5 + 20.25 = 25.25
20.25 + 9p + p2 = 25.25

Factor a perfect square on the left side:
(p + 4.5)(p + 4.5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(p + 4.5) equal to 5.024937811 and -5.024937811.


Subproblem 1
p + 4.5 = 5.024937811

Simplifying
p + 4.5 = 5.024937811

Reorder the terms:
4.5 + p = 5.024937811

Solving
4.5 + p = 5.024937811

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 = 5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = 5.024937811 + -4.5
p = 5.024937811 + -4.5

Combine like terms: 5.024937811 + -4.5 = 0.524937811
p = 0.524937811

Simplifying
p = 0.524937811


Subproblem 2
p + 4.5 = -5.024937811

Simplifying
p + 4.5 = -5.024937811

Reorder the terms:
4.5 + p = -5.024937811

Solving
4.5 + p = -5.024937811

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 = -5.024937811 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + p = -5.024937811 + -4.5
p = -5.024937811 + -4.5

Combine like terms: -5.024937811 + -4.5 = -9.524937811
p = -9.524937811

Simplifying
p = -9.524937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.524937811, -9.524937811}
Solution
p = {0.524937811, -9.524937811}

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