x^2-4.75x-0.125=0

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Solution for x^2-4.75x-0.125=0 equation: 


Simplifying
x2 + -4.75x + -0.125 = 0

Reorder the terms:
-0.125 + -4.75x + x2 = 0

Solving
-0.125 + -4.75x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -4.75x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -4.75x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -4.75x + x2 = 0 + 0.125
-4.75x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-4.75x + x2 = 0.125

The x term is -4.75x.  Take half its coefficient (-2.375).
Square it (5.640625) and add it to both sides.

Add '5.640625' to each side of the equation.
-4.75x + 5.640625 + x2 = 0.125 + 5.640625

Reorder the terms:
5.640625 + -4.75x + x2 = 0.125 + 5.640625

Combine like terms: 0.125 + 5.640625 = 5.765625
5.640625 + -4.75x + x2 = 5.765625

Factor a perfect square on the left side:
(x + -2.375)(x + -2.375) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + -2.375) equal to 2.401171589 and -2.401171589.


Subproblem 1
x + -2.375 = 2.401171589

Simplifying
x + -2.375 = 2.401171589

Reorder the terms:
-2.375 + x = 2.401171589

Solving
-2.375 + x = 2.401171589

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = 2.401171589 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = 2.401171589 + 2.375
x = 2.401171589 + 2.375

Combine like terms: 2.401171589 + 2.375 = 4.776171589
x = 4.776171589

Simplifying
x = 4.776171589


Subproblem 2
x + -2.375 = -2.401171589

Simplifying
x + -2.375 = -2.401171589

Reorder the terms:
-2.375 + x = -2.401171589

Solving
-2.375 + x = -2.401171589

Solving for variable 'x'.

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

Add '2.375' to each side of the equation.
-2.375 + 2.375 + x = -2.401171589 + 2.375

Combine like terms: -2.375 + 2.375 = 0.000
0.000 + x = -2.401171589 + 2.375
x = -2.401171589 + 2.375

Combine like terms: -2.401171589 + 2.375 = -0.026171589
x = -0.026171589

Simplifying
x = -0.026171589


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.776171589, -0.026171589}

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