-2p^2+20p+34=0

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Solution for -2p^2+20p+34=0 equation: 


Simplifying
-2p2 + 20p + 34 = 0

Reorder the terms:
34 + 20p + -2p2 = 0

Solving
34 + 20p + -2p2 = 0

Solving for variable 'p'.

Factor out the Greatest Common Factor (GCF), '2'.
2(17 + 10p + -1p2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(17 + 10p + -1p2)' equal to zero and attempt to solve:

Simplifying
17 + 10p + -1p2 = 0

Solving
17 + 10p + -1p2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-17 + -10p + p2 = 0

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -10p + 17 + p2 = 0 + 17

Reorder the terms:
-17 + 17 + -10p + p2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -10p + p2 = 0 + 17
-10p + p2 = 0 + 17

Combine like terms: 0 + 17 = 17
-10p + p2 = 17

The p term is -10p.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10p + 25 + p2 = 17 + 25

Reorder the terms:
25 + -10p + p2 = 17 + 25

Combine like terms: 17 + 25 = 42
25 + -10p + p2 = 42

Factor a perfect square on the left side:
(p + -5)(p + -5) = 42

Calculate the square root of the right side: 6.480740698

Break this problem into two subproblems by setting 
(p + -5) equal to 6.480740698 and -6.480740698.


Subproblem 1
p + -5 = 6.480740698

Simplifying
p + -5 = 6.480740698

Reorder the terms:
-5 + p = 6.480740698

Solving
-5 + p = 6.480740698

Solving for variable 'p'.

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

Add '5' to each side of the equation.
-5 + 5 + p = 6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + p = 6.480740698 + 5
p = 6.480740698 + 5

Combine like terms: 6.480740698 + 5 = 11.480740698
p = 11.480740698

Simplifying
p = 11.480740698


Subproblem 2
p + -5 = -6.480740698

Simplifying
p + -5 = -6.480740698

Reorder the terms:
-5 + p = -6.480740698

Solving
-5 + p = -6.480740698

Solving for variable 'p'.

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

Add '5' to each side of the equation.
-5 + 5 + p = -6.480740698 + 5

Combine like terms: -5 + 5 = 0
0 + p = -6.480740698 + 5
p = -6.480740698 + 5

Combine like terms: -6.480740698 + 5 = -1.480740698
p = -1.480740698

Simplifying
p = -1.480740698


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {11.480740698, -1.480740698}
Solution
p = {11.480740698, -1.480740698}

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