5-3x-18=1x(1-8x)

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Solution for 5-3x-18=1x(1-8x) equation:


Simplifying
5 + -3x + -18 = 1x(1 + -8x)

Reorder the terms:
5 + -18 + -3x = 1x(1 + -8x)

Combine like terms: 5 + -18 = -13
-13 + -3x = 1x(1 + -8x)
-13 + -3x = (1 * 1x + -8x * 1x)
-13 + -3x = (1x + -8x2)

Solving
-13 + -3x = 1x + -8x2

Solving for variable 'x'.

Combine like terms: -3x + -1x = -4x
-13 + -4x + 8x2 = 1x + -8x2 + -1x + 8x2

Reorder the terms:
-13 + -4x + 8x2 = 1x + -1x + -8x2 + 8x2

Combine like terms: 1x + -1x = 0
-13 + -4x + 8x2 = 0 + -8x2 + 8x2
-13 + -4x + 8x2 = -8x2 + 8x2

Combine like terms: -8x2 + 8x2 = 0
-13 + -4x + 8x2 = 0

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

Divide each side by '8'.
-1.625 + -0.5x + x2 = 0

Move the constant term to the right:

Add '1.625' to each side of the equation.
-1.625 + -0.5x + 1.625 + x2 = 0 + 1.625

Reorder the terms:
-1.625 + 1.625 + -0.5x + x2 = 0 + 1.625

Combine like terms: -1.625 + 1.625 = 0.000
0.000 + -0.5x + x2 = 0 + 1.625
-0.5x + x2 = 0 + 1.625

Combine like terms: 0 + 1.625 = 1.625
-0.5x + x2 = 1.625

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 = 1.625 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 1.625 + 0.0625

Combine like terms: 1.625 + 0.0625 = 1.6875
0.0625 + -0.5x + x2 = 1.6875

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 1.6875

Calculate the square root of the right side: 1.299038106

Break this problem into two subproblems by setting 
(x + -0.25) equal to 1.299038106 and -1.299038106.

Subproblem 1

x + -0.25 = 1.299038106 Simplifying x + -0.25 = 1.299038106 Reorder the terms: -0.25 + x = 1.299038106 Solving -0.25 + x = 1.299038106 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 = 1.299038106 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 1.299038106 + 0.25 x = 1.299038106 + 0.25 Combine like terms: 1.299038106 + 0.25 = 1.549038106 x = 1.549038106 Simplifying x = 1.549038106

Subproblem 2

x + -0.25 = -1.299038106 Simplifying x + -0.25 = -1.299038106 Reorder the terms: -0.25 + x = -1.299038106 Solving -0.25 + x = -1.299038106 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 = -1.299038106 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -1.299038106 + 0.25 x = -1.299038106 + 0.25 Combine like terms: -1.299038106 + 0.25 = -1.049038106 x = -1.049038106 Simplifying x = -1.049038106

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.549038106, -1.049038106}

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