4x^2-0.6x-0.5=0

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Solution for 4x^2-0.6x-0.5=0 equation: 


Simplifying
4x2 + -0.6x + -0.5 = 0

Reorder the terms:
-0.5 + -0.6x + 4x2 = 0

Solving
-0.5 + -0.6x + 4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-0.125 + -0.15x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.15x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.15x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.15x + x2 = 0 + 0.125
-0.15x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.15x + x2 = 0.125

The x term is -0.15x.  Take half its coefficient (-0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
-0.15x + 0.005625 + x2 = 0.125 + 0.005625

Reorder the terms:
0.005625 + -0.15x + x2 = 0.125 + 0.005625

Combine like terms: 0.125 + 0.005625 = 0.130625
0.005625 + -0.15x + x2 = 0.130625

Factor a perfect square on the left side:
(x + -0.075)(x + -0.075) = 0.130625

Calculate the square root of the right side: 0.361420807

Break this problem into two subproblems by setting 
(x + -0.075) equal to 0.361420807 and -0.361420807.


Subproblem 1
x + -0.075 = 0.361420807

Simplifying
x + -0.075 = 0.361420807

Reorder the terms:
-0.075 + x = 0.361420807

Solving
-0.075 + x = 0.361420807

Solving for variable 'x'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + x = 0.361420807 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + x = 0.361420807 + 0.075
x = 0.361420807 + 0.075

Combine like terms: 0.361420807 + 0.075 = 0.436420807
x = 0.436420807

Simplifying
x = 0.436420807


Subproblem 2
x + -0.075 = -0.361420807

Simplifying
x + -0.075 = -0.361420807

Reorder the terms:
-0.075 + x = -0.361420807

Solving
-0.075 + x = -0.361420807

Solving for variable 'x'.

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

Add '0.075' to each side of the equation.
-0.075 + 0.075 + x = -0.361420807 + 0.075

Combine like terms: -0.075 + 0.075 = 0.000
0.000 + x = -0.361420807 + 0.075
x = -0.361420807 + 0.075

Combine like terms: -0.361420807 + 0.075 = -0.286420807
x = -0.286420807

Simplifying
x = -0.286420807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.436420807, -0.286420807}

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