x^2+11x=18.75

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Solution for x^2+11x=18.75 equation: 


Simplifying
x2 + 11x = 18.75

Reorder the terms:
11x + x2 = 18.75

Solving
11x + x2 = 18.75

Solving for variable 'x'.

Reorder the terms:
-18.75 + 11x + x2 = 18.75 + -18.75

Combine like terms: 18.75 + -18.75 = 0.00
-18.75 + 11x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 11x + 18.75 + x2 = 0.00 + 18.75

Reorder the terms:
-18.75 + 18.75 + 11x + x2 = 0.00 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 11x + x2 = 0.00 + 18.75
11x + x2 = 0.00 + 18.75

Combine like terms: 0.00 + 18.75 = 18.75
11x + x2 = 18.75

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 18.75 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 18.75 + 30.25

Combine like terms: 18.75 + 30.25 = 49
30.25 + 11x + x2 = 49

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7 and -7.


Subproblem 1
x + 5.5 = 7

Simplifying
x + 5.5 = 7

Reorder the terms:
5.5 + x = 7

Solving
5.5 + x = 7

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 7 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 7 + -5.5
x = 7 + -5.5

Combine like terms: 7 + -5.5 = 1.5
x = 1.5

Simplifying
x = 1.5


Subproblem 2
x + 5.5 = -7

Simplifying
x + 5.5 = -7

Reorder the terms:
5.5 + x = -7

Solving
5.5 + x = -7

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -7 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -7 + -5.5
x = -7 + -5.5

Combine like terms: -7 + -5.5 = -12.5
x = -12.5

Simplifying
x = -12.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.5, -12.5}

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