x^2-x-15.75=0

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Solution for x^2-x-15.75=0 equation: 


Simplifying
x2 + -1x + -15.75 = 0

Reorder the terms:
-15.75 + -1x + x2 = 0

Solving
-15.75 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '15.75' to each side of the equation.
-15.75 + -1x + 15.75 + x2 = 0 + 15.75

Reorder the terms:
-15.75 + 15.75 + -1x + x2 = 0 + 15.75

Combine like terms: -15.75 + 15.75 = 0.00
0.00 + -1x + x2 = 0 + 15.75
-1x + x2 = 0 + 15.75

Combine like terms: 0 + 15.75 = 15.75
-1x + x2 = 15.75

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 15.75 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 15.75 + 0.25

Combine like terms: 15.75 + 0.25 = 16
0.25 + -1x + x2 = 16

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(x + -0.5) equal to 4 and -4.


Subproblem 1
x + -0.5 = 4

Simplifying
x + -0.5 = 4

Reorder the terms:
-0.5 + x = 4

Solving
-0.5 + x = 4

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 4 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 4 + 0.5
x = 4 + 0.5

Combine like terms: 4 + 0.5 = 4.5
x = 4.5

Simplifying
x = 4.5


Subproblem 2
x + -0.5 = -4

Simplifying
x + -0.5 = -4

Reorder the terms:
-0.5 + x = -4

Solving
-0.5 + x = -4

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -4 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -4 + 0.5
x = -4 + 0.5

Combine like terms: -4 + 0.5 = -3.5
x = -3.5

Simplifying
x = -3.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.5, -3.5}

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