x^2-3x-13.75=0

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Solution for x^2-3x-13.75=0 equation: 


Simplifying
x2 + -3x + -13.75 = 0

Reorder the terms:
-13.75 + -3x + x2 = 0

Solving
-13.75 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '13.75' to each side of the equation.
-13.75 + -3x + 13.75 + x2 = 0 + 13.75

Reorder the terms:
-13.75 + 13.75 + -3x + x2 = 0 + 13.75

Combine like terms: -13.75 + 13.75 = 0.00
0.00 + -3x + x2 = 0 + 13.75
-3x + x2 = 0 + 13.75

Combine like terms: 0 + 13.75 = 13.75
-3x + x2 = 13.75

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 = 13.75 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 13.75 + 2.25

Combine like terms: 13.75 + 2.25 = 16
2.25 + -3x + x2 = 16

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4 and -4.


Subproblem 1
x + -1.5 = 4

Simplifying
x + -1.5 = 4

Reorder the terms:
-1.5 + x = 4

Solving
-1.5 + x = 4

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 = 4 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4 + 1.5
x = 4 + 1.5

Combine like terms: 4 + 1.5 = 5.5
x = 5.5

Simplifying
x = 5.5


Subproblem 2
x + -1.5 = -4

Simplifying
x + -1.5 = -4

Reorder the terms:
-1.5 + x = -4

Solving
-1.5 + x = -4

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 = -4 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4 + 1.5
x = -4 + 1.5

Combine like terms: -4 + 1.5 = -2.5
x = -2.5

Simplifying
x = -2.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.5, -2.5}

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