x^2+1.25x-159=0

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Solution for x^2+1.25x-159=0 equation: 


Simplifying
x2 + 1.25x + -159 = 0

Reorder the terms:
-159 + 1.25x + x2 = 0

Solving
-159 + 1.25x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '159' to each side of the equation.
-159 + 1.25x + 159 + x2 = 0 + 159

Reorder the terms:
-159 + 159 + 1.25x + x2 = 0 + 159

Combine like terms: -159 + 159 = 0
0 + 1.25x + x2 = 0 + 159
1.25x + x2 = 0 + 159

Combine like terms: 0 + 159 = 159
1.25x + x2 = 159

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 159 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 159 + 0.390625

Combine like terms: 159 + 0.390625 = 159.390625
0.390625 + 1.25x + x2 = 159.390625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 159.390625

Calculate the square root of the right side: 12.625

Break this problem into two subproblems by setting 
(x + 0.625) equal to 12.625 and -12.625.


Subproblem 1
x + 0.625 = 12.625

Simplifying
x + 0.625 = 12.625

Reorder the terms:
0.625 + x = 12.625

Solving
0.625 + x = 12.625

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 12.625 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 12.625 + -0.625
x = 12.625 + -0.625

Combine like terms: 12.625 + -0.625 = 12
x = 12

Simplifying
x = 12


Subproblem 2
x + 0.625 = -12.625

Simplifying
x + 0.625 = -12.625

Reorder the terms:
0.625 + x = -12.625

Solving
0.625 + x = -12.625

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -12.625 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -12.625 + -0.625
x = -12.625 + -0.625

Combine like terms: -12.625 + -0.625 = -13.25
x = -13.25

Simplifying
x = -13.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12, -13.25}

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