17=3p(p-5)+8

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Solution for 17=3p(p-5)+8 equation: 


Simplifying
17 = 3p(p + -5) + 8

Reorder the terms:
17 = 3p(-5 + p) + 8
17 = (-5 * 3p + p * 3p) + 8
17 = (-15p + 3p2) + 8

Reorder the terms:
17 = 8 + -15p + 3p2

Solving
17 = 8 + -15p + 3p2

Solving for variable 'p'.

Combine like terms: 17 + -8 = 9
9 + 15p + -3p2 = 8 + -15p + 3p2 + -8 + 15p + -3p2

Reorder the terms:
9 + 15p + -3p2 = 8 + -8 + -15p + 15p + 3p2 + -3p2

Combine like terms: 8 + -8 = 0
9 + 15p + -3p2 = 0 + -15p + 15p + 3p2 + -3p2
9 + 15p + -3p2 = -15p + 15p + 3p2 + -3p2

Combine like terms: -15p + 15p = 0
9 + 15p + -3p2 = 0 + 3p2 + -3p2
9 + 15p + -3p2 = 3p2 + -3p2

Combine like terms: 3p2 + -3p2 = 0
9 + 15p + -3p2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 5p + -1p2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + 5p + -1p2)' equal to zero and attempt to solve:

Simplifying
3 + 5p + -1p2 = 0

Solving
3 + 5p + -1p2 = 0

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

Divide each side by '-1'.
-3 + -5p + p2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -5p + 3 + p2 = 0 + 3

Reorder the terms:
-3 + 3 + -5p + p2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5p + p2 = 0 + 3
-5p + p2 = 0 + 3

Combine like terms: 0 + 3 = 3
-5p + p2 = 3

The p term is -5p.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5p + 6.25 + p2 = 3 + 6.25

Reorder the terms:
6.25 + -5p + p2 = 3 + 6.25

Combine like terms: 3 + 6.25 = 9.25
6.25 + -5p + p2 = 9.25

Factor a perfect square on the left side:
(p + -2.5)(p + -2.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(p + -2.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
p + -2.5 = 3.041381265

Simplifying
p + -2.5 = 3.041381265

Reorder the terms:
-2.5 + p = 3.041381265

Solving
-2.5 + p = 3.041381265

Solving for variable 'p'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + p = 3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + p = 3.041381265 + 2.5
p = 3.041381265 + 2.5

Combine like terms: 3.041381265 + 2.5 = 5.541381265
p = 5.541381265

Simplifying
p = 5.541381265


Subproblem 2
p + -2.5 = -3.041381265

Simplifying
p + -2.5 = -3.041381265

Reorder the terms:
-2.5 + p = -3.041381265

Solving
-2.5 + p = -3.041381265

Solving for variable 'p'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + p = -3.041381265 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + p = -3.041381265 + 2.5
p = -3.041381265 + 2.5

Combine like terms: -3.041381265 + 2.5 = -0.541381265
p = -0.541381265

Simplifying
p = -0.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {5.541381265, -0.541381265}
Solution
p = {5.541381265, -0.541381265}

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