p^2-37p+30=0

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Solution for p^2-37p+30=0 equation: 


Simplifying
p2 + -37p + 30 = 0

Reorder the terms:
30 + -37p + p2 = 0

Solving
30 + -37p + p2 = 0

Solving for variable 'p'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -37p + -30 + p2 = 0 + -30

Reorder the terms:
30 + -30 + -37p + p2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -37p + p2 = 0 + -30
-37p + p2 = 0 + -30

Combine like terms: 0 + -30 = -30
-37p + p2 = -30

The p term is -37p.  Take half its coefficient (-18.5).
Square it (342.25) and add it to both sides.

Add '342.25' to each side of the equation.
-37p + 342.25 + p2 = -30 + 342.25

Reorder the terms:
342.25 + -37p + p2 = -30 + 342.25

Combine like terms: -30 + 342.25 = 312.25
342.25 + -37p + p2 = 312.25

Factor a perfect square on the left side:
(p + -18.5)(p + -18.5) = 312.25

Calculate the square root of the right side: 17.670597047

Break this problem into two subproblems by setting 
(p + -18.5) equal to 17.670597047 and -17.670597047.


Subproblem 1
p + -18.5 = 17.670597047

Simplifying
p + -18.5 = 17.670597047

Reorder the terms:
-18.5 + p = 17.670597047

Solving
-18.5 + p = 17.670597047

Solving for variable 'p'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + p = 17.670597047 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + p = 17.670597047 + 18.5
p = 17.670597047 + 18.5

Combine like terms: 17.670597047 + 18.5 = 36.170597047
p = 36.170597047

Simplifying
p = 36.170597047


Subproblem 2
p + -18.5 = -17.670597047

Simplifying
p + -18.5 = -17.670597047

Reorder the terms:
-18.5 + p = -17.670597047

Solving
-18.5 + p = -17.670597047

Solving for variable 'p'.

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

Add '18.5' to each side of the equation.
-18.5 + 18.5 + p = -17.670597047 + 18.5

Combine like terms: -18.5 + 18.5 = 0.0
0.0 + p = -17.670597047 + 18.5
p = -17.670597047 + 18.5

Combine like terms: -17.670597047 + 18.5 = 0.829402953
p = 0.829402953

Simplifying
p = 0.829402953


Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {36.170597047, 0.829402953}

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