1.5c^2+33c-75=52.50

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Solution for 1.5c^2+33c-75=52.50 equation: 


Simplifying
1.5c2 + 33c + -75 = 52.50

Reorder the terms:
-75 + 33c + 1.5c2 = 52.50

Solving
-75 + 33c + 1.5c2 = 52.50

Solving for variable 'c'.

Reorder the terms:
-75 + -52.50 + 33c + 1.5c2 = 52.50 + -52.50

Combine like terms: -75 + -52.50 = -127.5
-127.5 + 33c + 1.5c2 = 52.50 + -52.50

Combine like terms: 52.50 + -52.50 = 0.00
-127.5 + 33c + 1.5c2 = 0.00

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

Divide each side by '1.5'.
-85 + 22c + c2 = 0.0

Move the constant term to the right:

Add '85' to each side of the equation.
-85 + 22c + 85 + c2 = 0.0 + 85

Reorder the terms:
-85 + 85 + 22c + c2 = 0.0 + 85

Combine like terms: -85 + 85 = 0
0 + 22c + c2 = 0.0 + 85
22c + c2 = 0.0 + 85

Combine like terms: 0.0 + 85 = 85
22c + c2 = 85

The c term is 22c.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22c + 121 + c2 = 85 + 121

Reorder the terms:
121 + 22c + c2 = 85 + 121

Combine like terms: 85 + 121 = 206
121 + 22c + c2 = 206

Factor a perfect square on the left side:
(c + 11)(c + 11) = 206

Calculate the square root of the right side: 14.352700094

Break this problem into two subproblems by setting 
(c + 11) equal to 14.352700094 and -14.352700094.


Subproblem 1
c + 11 = 14.352700094

Simplifying
c + 11 = 14.352700094

Reorder the terms:
11 + c = 14.352700094

Solving
11 + c = 14.352700094

Solving for variable 'c'.

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

Add '-11' to each side of the equation.
11 + -11 + c = 14.352700094 + -11

Combine like terms: 11 + -11 = 0
0 + c = 14.352700094 + -11
c = 14.352700094 + -11

Combine like terms: 14.352700094 + -11 = 3.352700094
c = 3.352700094

Simplifying
c = 3.352700094


Subproblem 2
c + 11 = -14.352700094

Simplifying
c + 11 = -14.352700094

Reorder the terms:
11 + c = -14.352700094

Solving
11 + c = -14.352700094

Solving for variable 'c'.

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

Add '-11' to each side of the equation.
11 + -11 + c = -14.352700094 + -11

Combine like terms: 11 + -11 = 0
0 + c = -14.352700094 + -11
c = -14.352700094 + -11

Combine like terms: -14.352700094 + -11 = -25.352700094
c = -25.352700094

Simplifying
c = -25.352700094


Solution
The solution to the problem is based on the solutions
from the subproblems.
c = {3.352700094, -25.352700094}

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