-.4x^2+.2x=-2

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Solution for -.4x^2+.2x=-2 equation:


Simplifying
-0.4x2 + 0.2x = -2

Reorder the terms:
0.2x + -0.4x2 = -2

Solving
0.2x + -0.4x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 0.2x + -0.4x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 0.2x + -0.4x2 = 0

Begin completing the square.  Divide all terms by
-0.4 the coefficient of the squared term: 

Divide each side by '-0.4'.
-5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.5x + x2 = 0 + 5
-0.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.5x + x2 = 5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 5 + 0.0625

Combine like terms: 5 + 0.0625 = 5.0625
0.0625 + -0.5x + x2 = 5.0625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 5.0625

Calculate the square root of the right side: 2.25

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.25 and -2.25.

Subproblem 1

x + -0.25 = 2.25 Simplifying x + -0.25 = 2.25 Reorder the terms: -0.25 + x = 2.25 Solving -0.25 + x = 2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.25 + 0.25 x = 2.25 + 0.25 Combine like terms: 2.25 + 0.25 = 2.5 x = 2.5 Simplifying x = 2.5

Subproblem 2

x + -0.25 = -2.25 Simplifying x + -0.25 = -2.25 Reorder the terms: -0.25 + x = -2.25 Solving -0.25 + x = -2.25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.25 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.25 + 0.25 x = -2.25 + 0.25 Combine like terms: -2.25 + 0.25 = -2 x = -2 Simplifying x = -2

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5, -2}

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