2-0.25*4-x+0.25*x^2=0.2

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Solution for 2-0.25*4-x+0.25*x^2=0.2 equation:


Simplifying
2 + -0.25 * 4 + -1x + 0.25x2 = 0.2

Multiply -0.25 * 4
2 + -1 + -1x + 0.25x2 = 0.2

Combine like terms: 2 + -1 = 1
1 + -1x + 0.25x2 = 0.2

Solving
1 + -1x + 0.25x2 = 0.2

Solving for variable 'x'.

Reorder the terms:
1 + -0.2 + -1x + 0.25x2 = 0.2 + -0.2

Combine like terms: 1 + -0.2 = 0.8
0.8 + -1x + 0.25x2 = 0.2 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.8 + -1x + 0.25x2 = 0.0

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

Divide each side by '0.25'.
3.2 + -4x + x2 = 0

Move the constant term to the right:

Add '-3.2' to each side of the equation.
3.2 + -4x + -3.2 + x2 = 0 + -3.2

Reorder the terms:
3.2 + -3.2 + -4x + x2 = 0 + -3.2

Combine like terms: 3.2 + -3.2 = 0.0
0.0 + -4x + x2 = 0 + -3.2
-4x + x2 = 0 + -3.2

Combine like terms: 0 + -3.2 = -3.2
-4x + x2 = -3.2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -3.2 + 4

Reorder the terms:
4 + -4x + x2 = -3.2 + 4

Combine like terms: -3.2 + 4 = 0.8
4 + -4x + x2 = 0.8

Factor a perfect square on the left side:
(x + -2)(x + -2) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
(x + -2) equal to 0.894427191 and -0.894427191.

Subproblem 1

x + -2 = 0.894427191 Simplifying x + -2 = 0.894427191 Reorder the terms: -2 + x = 0.894427191 Solving -2 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.894427191 + 2 x = 0.894427191 + 2 Combine like terms: 0.894427191 + 2 = 2.894427191 x = 2.894427191 Simplifying x = 2.894427191

Subproblem 2

x + -2 = -0.894427191 Simplifying x + -2 = -0.894427191 Reorder the terms: -2 + x = -0.894427191 Solving -2 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -0.894427191 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.894427191 + 2 x = -0.894427191 + 2 Combine like terms: -0.894427191 + 2 = 1.105572809 x = 1.105572809 Simplifying x = 1.105572809

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.894427191, 1.105572809}

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