8x(x-2)=1+8x

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Solution for 8x(x-2)=1+8x equation:


Simplifying
8x(x + -2) = 1 + 8x

Reorder the terms:
8x(-2 + x) = 1 + 8x
(-2 * 8x + x * 8x) = 1 + 8x
(-16x + 8x2) = 1 + 8x

Solving
-16x + 8x2 = 1 + 8x

Solving for variable 'x'.

Reorder the terms:
-1 + -16x + -8x + 8x2 = 1 + 8x + -1 + -8x

Combine like terms: -16x + -8x = -24x
-1 + -24x + 8x2 = 1 + 8x + -1 + -8x

Reorder the terms:
-1 + -24x + 8x2 = 1 + -1 + 8x + -8x

Combine like terms: 1 + -1 = 0
-1 + -24x + 8x2 = 0 + 8x + -8x
-1 + -24x + 8x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-1 + -24x + 8x2 = 0

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

Divide each side by '8'.
-0.125 + -3x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -3x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -3x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -3x + x2 = 0 + 0.125
-3x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-3x + x2 = 0.125

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 0.125 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.125 + 2.25

Combine like terms: 0.125 + 2.25 = 2.375
2.25 + -3x + x2 = 2.375

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 2.375

Calculate the square root of the right side: 1.541103501

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.541103501 and -1.541103501.

Subproblem 1

x + -1.5 = 1.541103501 Simplifying x + -1.5 = 1.541103501 Reorder the terms: -1.5 + x = 1.541103501 Solving -1.5 + x = 1.541103501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.541103501 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.541103501 + 1.5 x = 1.541103501 + 1.5 Combine like terms: 1.541103501 + 1.5 = 3.041103501 x = 3.041103501 Simplifying x = 3.041103501

Subproblem 2

x + -1.5 = -1.541103501 Simplifying x + -1.5 = -1.541103501 Reorder the terms: -1.5 + x = -1.541103501 Solving -1.5 + x = -1.541103501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.541103501 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.541103501 + 1.5 x = -1.541103501 + 1.5 Combine like terms: -1.541103501 + 1.5 = -0.041103501 x = -0.041103501 Simplifying x = -0.041103501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.041103501, -0.041103501}

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