x^2+3x-118.75=0

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Solution for x^2+3x-118.75=0 equation: 


Simplifying
x2 + 3x + -118.75 = 0

Reorder the terms:
-118.75 + 3x + x2 = 0

Solving
-118.75 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '118.75' to each side of the equation.
-118.75 + 3x + 118.75 + x2 = 0 + 118.75

Reorder the terms:
-118.75 + 118.75 + 3x + x2 = 0 + 118.75

Combine like terms: -118.75 + 118.75 = 0.00
0.00 + 3x + x2 = 0 + 118.75
3x + x2 = 0 + 118.75

Combine like terms: 0 + 118.75 = 118.75
3x + x2 = 118.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 118.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 118.75 + 2.25

Combine like terms: 118.75 + 2.25 = 121
2.25 + 3x + x2 = 121

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 121

Calculate the square root of the right side: 11

Break this problem into two subproblems by setting 
(x + 1.5) equal to 11 and -11.


Subproblem 1
x + 1.5 = 11

Simplifying
x + 1.5 = 11

Reorder the terms:
1.5 + x = 11

Solving
1.5 + x = 11

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = 11 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = 11 + -1.5
x = 11 + -1.5

Combine like terms: 11 + -1.5 = 9.5
x = 9.5

Simplifying
x = 9.5


Subproblem 2
x + 1.5 = -11

Simplifying
x + 1.5 = -11

Reorder the terms:
1.5 + x = -11

Solving
1.5 + x = -11

Solving for variable 'x'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + x = -11 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + x = -11 + -1.5
x = -11 + -1.5

Combine like terms: -11 + -1.5 = -12.5
x = -12.5

Simplifying
x = -12.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.5, -12.5}

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