0.2x^2-0.4x-1=1-3x

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Solution for 0.2x^2-0.4x-1=1-3x equation:


Simplifying
0.2x2 + -0.4x + -1 = 1 + -3x

Reorder the terms:
-1 + -0.4x + 0.2x2 = 1 + -3x

Solving
-1 + -0.4x + 0.2x2 = 1 + -3x

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + -0.4x + 3x + 0.2x2 = 1 + -3x + -1 + 3x

Combine like terms: -1 + -1 = -2
-2 + -0.4x + 3x + 0.2x2 = 1 + -3x + -1 + 3x

Combine like terms: -0.4x + 3x = 2.6x
-2 + 2.6x + 0.2x2 = 1 + -3x + -1 + 3x

Reorder the terms:
-2 + 2.6x + 0.2x2 = 1 + -1 + -3x + 3x

Combine like terms: 1 + -1 = 0
-2 + 2.6x + 0.2x2 = 0 + -3x + 3x
-2 + 2.6x + 0.2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-2 + 2.6x + 0.2x2 = 0

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

Divide each side by '0.2'.
-10 + 13x + x2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 13x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + 13x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 13x + x2 = 0 + 10
13x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
13x + x2 = 10

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 10 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 10 + 42.25

Combine like terms: 10 + 42.25 = 52.25
42.25 + 13x + x2 = 52.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 6.5) equal to 7.228416147 and -7.228416147.

Subproblem 1

x + 6.5 = 7.228416147 Simplifying x + 6.5 = 7.228416147 Reorder the terms: 6.5 + x = 7.228416147 Solving 6.5 + x = 7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 7.228416147 + -6.5 x = 7.228416147 + -6.5 Combine like terms: 7.228416147 + -6.5 = 0.728416147 x = 0.728416147 Simplifying x = 0.728416147

Subproblem 2

x + 6.5 = -7.228416147 Simplifying x + 6.5 = -7.228416147 Reorder the terms: 6.5 + x = -7.228416147 Solving 6.5 + x = -7.228416147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -7.228416147 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -7.228416147 + -6.5 x = -7.228416147 + -6.5 Combine like terms: -7.228416147 + -6.5 = -13.728416147 x = -13.728416147 Simplifying x = -13.728416147

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.728416147, -13.728416147}

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