.6x^2-4x-3.75=0

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Solution for .6x^2-4x-3.75=0 equation: 


Simplifying
0.6x2 + -4x + -3.75 = 0

Reorder the terms:
-3.75 + -4x + 0.6x2 = 0

Solving
-3.75 + -4x + 0.6x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.6'.
-6.25 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -6.666666667x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -6.666666667x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -6.666666667x + x2 = 0 + 6.25
-6.666666667x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-6.666666667x + x2 = 6.25

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 6.25 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 6.25 + 11.11111112

Combine like terms: 6.25 + 11.11111112 = 17.36111112
11.11111112 + -6.666666667x + x2 = 17.36111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 17.36111112

Calculate the square root of the right side: 4.166666668

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 4.166666668 and -4.166666668.


Subproblem 1
x + -3.333333334 = 4.166666668

Simplifying
x + -3.333333334 = 4.166666668

Reorder the terms:
-3.333333334 + x = 4.166666668

Solving
-3.333333334 + x = 4.166666668

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 4.166666668 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 4.166666668 + 3.333333334
x = 4.166666668 + 3.333333334

Combine like terms: 4.166666668 + 3.333333334 = 7.500000002
x = 7.500000002

Simplifying
x = 7.500000002


Subproblem 2
x + -3.333333334 = -4.166666668

Simplifying
x + -3.333333334 = -4.166666668

Reorder the terms:
-3.333333334 + x = -4.166666668

Solving
-3.333333334 + x = -4.166666668

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -4.166666668 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -4.166666668 + 3.333333334
x = -4.166666668 + 3.333333334

Combine like terms: -4.166666668 + 3.333333334 = -0.833333334
x = -0.833333334

Simplifying
x = -0.833333334


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.500000002, -0.833333334}

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