0.0080789=x*(1-12.353x)

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Solution for 0.0080789=x*(1-12.353x) equation:


Simplifying
0.0080789 = x(1 + -12.353x)
0.0080789 = (1 * x + -12.353x * x)
0.0080789 = (1x + -12.353x2)

Solving
0.0080789 = 1x + -12.353x2

Solving for variable 'x'.

Reorder the terms:
0.0080789 + -1x + 12.353x2 = 1x + -1x + -12.353x2 + 12.353x2

Combine like terms: 1x + -1x = 0
0.0080789 + -1x + 12.353x2 = 0 + -12.353x2 + 12.353x2
0.0080789 + -1x + 12.353x2 = -12.353x2 + 12.353x2

Combine like terms: -12.353x2 + 12.353x2 = 0.000
0.0080789 + -1x + 12.353x2 = 0.000

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

Divide each side by '12.353'.
0.0006540030762 + -0.08095199547x + x2 = 0

Move the constant term to the right:

Add '-0.0006540030762' to each side of the equation.
0.0006540030762 + -0.08095199547x + -0.0006540030762 + x2 = 0 + -0.0006540030762

Reorder the terms:
0.0006540030762 + -0.0006540030762 + -0.08095199547x + x2 = 0 + -0.0006540030762

Combine like terms: 0.0006540030762 + -0.0006540030762 = 0.0000000000000
0.0000000000000 + -0.08095199547x + x2 = 0 + -0.0006540030762
-0.08095199547x + x2 = 0 + -0.0006540030762

Combine like terms: 0 + -0.0006540030762 = -0.0006540030762
-0.08095199547x + x2 = -0.0006540030762

The x term is -0.08095199547x.  Take half its coefficient (-0.04047599774).
Square it (0.001638306393) and add it to both sides.

Add '0.001638306393' to each side of the equation.
-0.08095199547x + 0.001638306393 + x2 = -0.0006540030762 + 0.001638306393

Reorder the terms:
0.001638306393 + -0.08095199547x + x2 = -0.0006540030762 + 0.001638306393

Combine like terms: -0.0006540030762 + 0.001638306393 = 0.0009843033168
0.001638306393 + -0.08095199547x + x2 = 0.0009843033168

Factor a perfect square on the left side:
(x + -0.04047599774)(x + -0.04047599774) = 0.0009843033168

Calculate the square root of the right side: 0.031373609

Break this problem into two subproblems by setting 
(x + -0.04047599774) equal to 0.031373609 and -0.031373609.

Subproblem 1

x + -0.04047599774 = 0.031373609 Simplifying x + -0.04047599774 = 0.031373609 Reorder the terms: -0.04047599774 + x = 0.031373609 Solving -0.04047599774 + x = 0.031373609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04047599774' to each side of the equation. -0.04047599774 + 0.04047599774 + x = 0.031373609 + 0.04047599774 Combine like terms: -0.04047599774 + 0.04047599774 = 0.00000000000 0.00000000000 + x = 0.031373609 + 0.04047599774 x = 0.031373609 + 0.04047599774 Combine like terms: 0.031373609 + 0.04047599774 = 0.07184960674 x = 0.07184960674 Simplifying x = 0.07184960674

Subproblem 2

x + -0.04047599774 = -0.031373609 Simplifying x + -0.04047599774 = -0.031373609 Reorder the terms: -0.04047599774 + x = -0.031373609 Solving -0.04047599774 + x = -0.031373609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04047599774' to each side of the equation. -0.04047599774 + 0.04047599774 + x = -0.031373609 + 0.04047599774 Combine like terms: -0.04047599774 + 0.04047599774 = 0.00000000000 0.00000000000 + x = -0.031373609 + 0.04047599774 x = -0.031373609 + 0.04047599774 Combine like terms: -0.031373609 + 0.04047599774 = 0.00910238874 x = 0.00910238874 Simplifying x = 0.00910238874

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.07184960674, 0.00910238874}

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