x^2+0.06x-0.8=0

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Solution for x^2+0.06x-0.8=0 equation:


Simplifying
x2 + 0.06x + -0.8 = 0

Reorder the terms:
-0.8 + 0.06x + x2 = 0

Solving
-0.8 + 0.06x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 0.06x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 0.06x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 0.06x + x2 = 0 + 0.8
0.06x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
0.06x + x2 = 0.8

The x term is 0.06x.  Take half its coefficient (0.03).
Square it (0.0009) and add it to both sides.

Add '0.0009' to each side of the equation.
0.06x + 0.0009 + x2 = 0.8 + 0.0009

Reorder the terms:
0.0009 + 0.06x + x2 = 0.8 + 0.0009

Combine like terms: 0.8 + 0.0009 = 0.8009
0.0009 + 0.06x + x2 = 0.8009

Factor a perfect square on the left side:
(x + 0.03)(x + 0.03) = 0.8009

Calculate the square root of the right side: 0.894930165

Break this problem into two subproblems by setting 
(x + 0.03) equal to 0.894930165 and -0.894930165.

Subproblem 1

x + 0.03 = 0.894930165 Simplifying x + 0.03 = 0.894930165 Reorder the terms: 0.03 + x = 0.894930165 Solving 0.03 + x = 0.894930165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = 0.894930165 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = 0.894930165 + -0.03 x = 0.894930165 + -0.03 Combine like terms: 0.894930165 + -0.03 = 0.864930165 x = 0.864930165 Simplifying x = 0.864930165

Subproblem 2

x + 0.03 = -0.894930165 Simplifying x + 0.03 = -0.894930165 Reorder the terms: 0.03 + x = -0.894930165 Solving 0.03 + x = -0.894930165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03' to each side of the equation. 0.03 + -0.03 + x = -0.894930165 + -0.03 Combine like terms: 0.03 + -0.03 = 0.00 0.00 + x = -0.894930165 + -0.03 x = -0.894930165 + -0.03 Combine like terms: -0.894930165 + -0.03 = -0.924930165 x = -0.924930165 Simplifying x = -0.924930165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.864930165, -0.924930165}

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