3x^2-8x-1.25=0

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Solution for 3x^2-8x-1.25=0 equation: 


Simplifying
3x2 + -8x + -1.25 = 0

Reorder the terms:
-1.25 + -8x + 3x2 = 0

Solving
-1.25 + -8x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-0.4166666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -2.666666667x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -2.666666667x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + 0.4166666667
-2.666666667x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-2.666666667x + x2 = 0.4166666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 0.4166666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 0.4166666667 + 1.777777780

Combine like terms: 0.4166666667 + 1.777777780 = 2.1944444467
1.777777780 + -2.666666667x + x2 = 2.1944444467

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 2.1944444467

Calculate the square root of the right side: 1.481365737

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.481365737 and -1.481365737.


Subproblem 1
x + -1.333333334 = 1.481365737

Simplifying
x + -1.333333334 = 1.481365737

Reorder the terms:
-1.333333334 + x = 1.481365737

Solving
-1.333333334 + x = 1.481365737

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = 1.481365737 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 1.481365737 + 1.333333334
x = 1.481365737 + 1.333333334

Combine like terms: 1.481365737 + 1.333333334 = 2.814699071
x = 2.814699071

Simplifying
x = 2.814699071


Subproblem 2
x + -1.333333334 = -1.481365737

Simplifying
x + -1.333333334 = -1.481365737

Reorder the terms:
-1.333333334 + x = -1.481365737

Solving
-1.333333334 + x = -1.481365737

Solving for variable 'x'.

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

Add '1.333333334' to each side of the equation.
-1.333333334 + 1.333333334 + x = -1.481365737 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -1.481365737 + 1.333333334
x = -1.481365737 + 1.333333334

Combine like terms: -1.481365737 + 1.333333334 = -0.148032403
x = -0.148032403

Simplifying
x = -0.148032403


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.814699071, -0.148032403}

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