2x^2-1.2x-1.6=0

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Solution for 2x^2-1.2x-1.6=0 equation:


Simplifying
2x2 + -1.2x + -1.6 = 0

Reorder the terms:
-1.6 + -1.2x + 2x2 = 0

Solving
-1.6 + -1.2x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-0.8 + -0.6x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + -0.6x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + -0.6x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + -0.6x + x2 = 0 + 0.8
-0.6x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
-0.6x + x2 = 0.8

The x term is -0.6x.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6x + 0.09 + x2 = 0.8 + 0.09

Reorder the terms:
0.09 + -0.6x + x2 = 0.8 + 0.09

Combine like terms: 0.8 + 0.09 = 0.89
0.09 + -0.6x + x2 = 0.89

Factor a perfect square on the left side:
(x + -0.3)(x + -0.3) = 0.89

Calculate the square root of the right side: 0.943398113

Break this problem into two subproblems by setting 
(x + -0.3) equal to 0.943398113 and -0.943398113.

Subproblem 1

x + -0.3 = 0.943398113 Simplifying x + -0.3 = 0.943398113 Reorder the terms: -0.3 + x = 0.943398113 Solving -0.3 + x = 0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = 0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = 0.943398113 + 0.3 x = 0.943398113 + 0.3 Combine like terms: 0.943398113 + 0.3 = 1.243398113 x = 1.243398113 Simplifying x = 1.243398113

Subproblem 2

x + -0.3 = -0.943398113 Simplifying x + -0.3 = -0.943398113 Reorder the terms: -0.3 + x = -0.943398113 Solving -0.3 + x = -0.943398113 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + x = -0.943398113 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + x = -0.943398113 + 0.3 x = -0.943398113 + 0.3 Combine like terms: -0.943398113 + 0.3 = -0.643398113 x = -0.643398113 Simplifying x = -0.643398113

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.243398113, -0.643398113}

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