0.6X^2-5.8X-5.7=0

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Solution for 0.6X^2-5.8X-5.7=0 equation: 


Simplifying
0.6X2 + -5.8X + -5.7 = 0

Reorder the terms:
-5.7 + -5.8X + 0.6X2 = 0

Solving
-5.7 + -5.8X + 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'.
-9.5 + -9.666666667X + X2 = 0

Move the constant term to the right:

Add '9.5' to each side of the equation.
-9.5 + -9.666666667X + 9.5 + X2 = 0 + 9.5

Reorder the terms:
-9.5 + 9.5 + -9.666666667X + X2 = 0 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + -9.666666667X + X2 = 0 + 9.5
-9.666666667X + X2 = 0 + 9.5

Combine like terms: 0 + 9.5 = 9.5
-9.666666667X + X2 = 9.5

The X term is -9.666666667X.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667X + 23.36111112 + X2 = 9.5 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667X + X2 = 9.5 + 23.36111112

Combine like terms: 9.5 + 23.36111112 = 32.86111112
23.36111112 + -9.666666667X + X2 = 32.86111112

Factor a perfect square on the left side:
(X + -4.833333334)(X + -4.833333334) = 32.86111112

Calculate the square root of the right side: 5.732461175

Break this problem into two subproblems by setting 
(X + -4.833333334) equal to 5.732461175 and -5.732461175.


Subproblem 1
X + -4.833333334 = 5.732461175

Simplifying
X + -4.833333334 = 5.732461175

Reorder the terms:
-4.833333334 + X = 5.732461175

Solving
-4.833333334 + X = 5.732461175

Solving for variable 'X'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + X = 5.732461175 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + X = 5.732461175 + 4.833333334
X = 5.732461175 + 4.833333334

Combine like terms: 5.732461175 + 4.833333334 = 10.565794509
X = 10.565794509

Simplifying
X = 10.565794509


Subproblem 2
X + -4.833333334 = -5.732461175

Simplifying
X + -4.833333334 = -5.732461175

Reorder the terms:
-4.833333334 + X = -5.732461175

Solving
-4.833333334 + X = -5.732461175

Solving for variable 'X'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + X = -5.732461175 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + X = -5.732461175 + 4.833333334
X = -5.732461175 + 4.833333334

Combine like terms: -5.732461175 + 4.833333334 = -0.899127841
X = -0.899127841

Simplifying
X = -0.899127841


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {10.565794509, -0.899127841}

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