x^2+3.5x=135

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Solution for x^2+3.5x=135 equation: 


Simplifying
x2 + 3.5x = 135

Reorder the terms:
3.5x + x2 = 135

Solving
3.5x + x2 = 135

Solving for variable 'x'.

Reorder the terms:
-135 + 3.5x + x2 = 135 + -135

Combine like terms: 135 + -135 = 0
-135 + 3.5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + 3.5x + 135 + x2 = 0 + 135

Reorder the terms:
-135 + 135 + 3.5x + x2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + 3.5x + x2 = 0 + 135
3.5x + x2 = 0 + 135

Combine like terms: 0 + 135 = 135
3.5x + x2 = 135

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = 135 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 135 + 3.0625

Combine like terms: 135 + 3.0625 = 138.0625
3.0625 + 3.5x + x2 = 138.0625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 138.0625

Calculate the square root of the right side: 11.75

Break this problem into two subproblems by setting 
(x + 1.75) equal to 11.75 and -11.75.


Subproblem 1
x + 1.75 = 11.75

Simplifying
x + 1.75 = 11.75

Reorder the terms:
1.75 + x = 11.75

Solving
1.75 + x = 11.75

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 11.75 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 11.75 + -1.75
x = 11.75 + -1.75

Combine like terms: 11.75 + -1.75 = 10
x = 10

Simplifying
x = 10


Subproblem 2
x + 1.75 = -11.75

Simplifying
x + 1.75 = -11.75

Reorder the terms:
1.75 + x = -11.75

Solving
1.75 + x = -11.75

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -11.75 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -11.75 + -1.75
x = -11.75 + -1.75

Combine like terms: -11.75 + -1.75 = -13.5
x = -13.5

Simplifying
x = -13.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10, -13.5}

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