-11x+2x(x-4)+8x=2x-8

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Solution for -11x+2x(x-4)+8x=2x-8 equation:


Simplifying
-11x + 2x(x + -4) + 8x = 2x + -8

Reorder the terms:
-11x + 2x(-4 + x) + 8x = 2x + -8
-11x + (-4 * 2x + x * 2x) + 8x = 2x + -8
-11x + (-8x + 2x2) + 8x = 2x + -8

Reorder the terms:
-11x + -8x + 8x + 2x2 = 2x + -8

Combine like terms: -11x + -8x = -19x
-19x + 8x + 2x2 = 2x + -8

Combine like terms: -19x + 8x = -11x
-11x + 2x2 = 2x + -8

Reorder the terms:
-11x + 2x2 = -8 + 2x

Solving
-11x + 2x2 = -8 + 2x

Solving for variable 'x'.

Reorder the terms:
8 + -11x + -2x + 2x2 = -8 + 2x + 8 + -2x

Combine like terms: -11x + -2x = -13x
8 + -13x + 2x2 = -8 + 2x + 8 + -2x

Reorder the terms:
8 + -13x + 2x2 = -8 + 8 + 2x + -2x

Combine like terms: -8 + 8 = 0
8 + -13x + 2x2 = 0 + 2x + -2x
8 + -13x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
8 + -13x + 2x2 = 0

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

Divide each side by '2'.
4 + -6.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6.5x + x2 = 0 + -4
-6.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6.5x + x2 = -4

The x term is -6.5x.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5x + 10.5625 + x2 = -4 + 10.5625

Reorder the terms:
10.5625 + -6.5x + x2 = -4 + 10.5625

Combine like terms: -4 + 10.5625 = 6.5625
10.5625 + -6.5x + x2 = 6.5625

Factor a perfect square on the left side:
(x + -3.25)(x + -3.25) = 6.5625

Calculate the square root of the right side: 2.561737691

Break this problem into two subproblems by setting 
(x + -3.25) equal to 2.561737691 and -2.561737691.

Subproblem 1

x + -3.25 = 2.561737691 Simplifying x + -3.25 = 2.561737691 Reorder the terms: -3.25 + x = 2.561737691 Solving -3.25 + x = 2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 2.561737691 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 2.561737691 + 3.25 x = 2.561737691 + 3.25 Combine like terms: 2.561737691 + 3.25 = 5.811737691 x = 5.811737691 Simplifying x = 5.811737691

Subproblem 2

x + -3.25 = -2.561737691 Simplifying x + -3.25 = -2.561737691 Reorder the terms: -3.25 + x = -2.561737691 Solving -3.25 + x = -2.561737691 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -2.561737691 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -2.561737691 + 3.25 x = -2.561737691 + 3.25 Combine like terms: -2.561737691 + 3.25 = 0.688262309 x = 0.688262309 Simplifying x = 0.688262309

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.811737691, 0.688262309}

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