x^2-5*x-12=0.5

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Solution for x^2-5*x-12=0.5 equation: 


Simplifying
x2 + -5x + -12 = 0.5

Reorder the terms:
-12 + -5x + x2 = 0.5

Solving
-12 + -5x + x2 = 0.5

Solving for variable 'x'.

Reorder the terms:
-12 + -0.5 + -5x + x2 = 0.5 + -0.5

Combine like terms: -12 + -0.5 = -12.5
-12.5 + -5x + x2 = 0.5 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
-12.5 + -5x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '12.5' to each side of the equation.
-12.5 + -5x + 12.5 + x2 = 0.0 + 12.5

Reorder the terms:
-12.5 + 12.5 + -5x + x2 = 0.0 + 12.5

Combine like terms: -12.5 + 12.5 = 0.0
0.0 + -5x + x2 = 0.0 + 12.5
-5x + x2 = 0.0 + 12.5

Combine like terms: 0.0 + 12.5 = 12.5
-5x + x2 = 12.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 12.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 12.5 + 6.25

Combine like terms: 12.5 + 6.25 = 18.75
6.25 + -5x + x2 = 18.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 18.75

Calculate the square root of the right side: 4.330127019

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.330127019 and -4.330127019.


Subproblem 1
x + -2.5 = 4.330127019

Simplifying
x + -2.5 = 4.330127019

Reorder the terms:
-2.5 + x = 4.330127019

Solving
-2.5 + x = 4.330127019

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.330127019 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.330127019 + 2.5
x = 4.330127019 + 2.5

Combine like terms: 4.330127019 + 2.5 = 6.830127019
x = 6.830127019

Simplifying
x = 6.830127019


Subproblem 2
x + -2.5 = -4.330127019

Simplifying
x + -2.5 = -4.330127019

Reorder the terms:
-2.5 + x = -4.330127019

Solving
-2.5 + x = -4.330127019

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.330127019 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.330127019 + 2.5
x = -4.330127019 + 2.5

Combine like terms: -4.330127019 + 2.5 = -1.830127019
x = -1.830127019

Simplifying
x = -1.830127019


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.830127019, -1.830127019}

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