.06(1-x)+.2x(x-5)=10

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Solution for .06(1-x)+.2x(x-5)=10 equation: 


Simplifying
0.06(1 + -1x) + 0.2x(x + -5) = 10
(1 * 0.06 + -1x * 0.06) + 0.2x(x + -5) = 10
(0.06 + -0.06x) + 0.2x(x + -5) = 10

Reorder the terms:
0.06 + -0.06x + 0.2x(-5 + x) = 10
0.06 + -0.06x + (-5 * 0.2x + x * 0.2x) = 10
0.06 + -0.06x + (-1x + 0.2x2) = 10

Combine like terms: -0.06x + -1x = -1.06x
0.06 + -1.06x + 0.2x2 = 10

Solving
0.06 + -1.06x + 0.2x2 = 10

Solving for variable 'x'.

Reorder the terms:
0.06 + -10 + -1.06x + 0.2x2 = 10 + -10

Combine like terms: 0.06 + -10 = -9.94
-9.94 + -1.06x + 0.2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-9.94 + -1.06x + 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'.
-49.7 + -5.3x + x2 = 0

Move the constant term to the right:

Add '49.7' to each side of the equation.
-49.7 + -5.3x + 49.7 + x2 = 0 + 49.7

Reorder the terms:
-49.7 + 49.7 + -5.3x + x2 = 0 + 49.7

Combine like terms: -49.7 + 49.7 = 0.0
0.0 + -5.3x + x2 = 0 + 49.7
-5.3x + x2 = 0 + 49.7

Combine like terms: 0 + 49.7 = 49.7
-5.3x + x2 = 49.7

The x term is -5.3x.  Take half its coefficient (-2.65).
Square it (7.0225) and add it to both sides.

Add '7.0225' to each side of the equation.
-5.3x + 7.0225 + x2 = 49.7 + 7.0225

Reorder the terms:
7.0225 + -5.3x + x2 = 49.7 + 7.0225

Combine like terms: 49.7 + 7.0225 = 56.7225
7.0225 + -5.3x + x2 = 56.7225

Factor a perfect square on the left side:
(x + -2.65)(x + -2.65) = 56.7225

Calculate the square root of the right side: 7.531434126

Break this problem into two subproblems by setting 
(x + -2.65) equal to 7.531434126 and -7.531434126.


Subproblem 1
x + -2.65 = 7.531434126

Simplifying
x + -2.65 = 7.531434126

Reorder the terms:
-2.65 + x = 7.531434126

Solving
-2.65 + x = 7.531434126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.65' to each side of the equation.
-2.65 + 2.65 + x = 7.531434126 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + x = 7.531434126 + 2.65
x = 7.531434126 + 2.65

Combine like terms: 7.531434126 + 2.65 = 10.181434126
x = 10.181434126

Simplifying
x = 10.181434126


Subproblem 2
x + -2.65 = -7.531434126

Simplifying
x + -2.65 = -7.531434126

Reorder the terms:
-2.65 + x = -7.531434126

Solving
-2.65 + x = -7.531434126

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.65' to each side of the equation.
-2.65 + 2.65 + x = -7.531434126 + 2.65

Combine like terms: -2.65 + 2.65 = 0.00
0.00 + x = -7.531434126 + 2.65
x = -7.531434126 + 2.65

Combine like terms: -7.531434126 + 2.65 = -4.881434126
x = -4.881434126

Simplifying
x = -4.881434126


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.181434126, -4.881434126}

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