x^2+3.5x-11.5=0

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Solution for x^2+3.5x-11.5=0 equation: 


Simplifying
x2 + 3.5x + -11.5 = 0

Reorder the terms:
-11.5 + 3.5x + x2 = 0

Solving
-11.5 + 3.5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + 3.5x + 11.5 + x2 = 0 + 11.5

Reorder the terms:
-11.5 + 11.5 + 3.5x + x2 = 0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + 3.5x + x2 = 0 + 11.5
3.5x + x2 = 0 + 11.5

Combine like terms: 0 + 11.5 = 11.5
3.5x + x2 = 11.5

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 = 11.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = 11.5 + 3.0625

Combine like terms: 11.5 + 3.0625 = 14.5625
3.0625 + 3.5x + x2 = 14.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(x + 1.75) equal to 3.816084381 and -3.816084381.


Subproblem 1
x + 1.75 = 3.816084381

Simplifying
x + 1.75 = 3.816084381

Reorder the terms:
1.75 + x = 3.816084381

Solving
1.75 + x = 3.816084381

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 = 3.816084381 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 3.816084381 + -1.75
x = 3.816084381 + -1.75

Combine like terms: 3.816084381 + -1.75 = 2.066084381
x = 2.066084381

Simplifying
x = 2.066084381


Subproblem 2
x + 1.75 = -3.816084381

Simplifying
x + 1.75 = -3.816084381

Reorder the terms:
1.75 + x = -3.816084381

Solving
1.75 + x = -3.816084381

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 = -3.816084381 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -3.816084381 + -1.75
x = -3.816084381 + -1.75

Combine like terms: -3.816084381 + -1.75 = -5.566084381
x = -5.566084381

Simplifying
x = -5.566084381


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.066084381, -5.566084381}

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