-9x(x-4)+8=4(3x-2)+8

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Solution for -9x(x-4)+8=4(3x-2)+8 equation:


Simplifying
-9x(x + -4) + 8 = 4(3x + -2) + 8

Reorder the terms:
-9x(-4 + x) + 8 = 4(3x + -2) + 8
(-4 * -9x + x * -9x) + 8 = 4(3x + -2) + 8
(36x + -9x2) + 8 = 4(3x + -2) + 8

Reorder the terms:
8 + 36x + -9x2 = 4(3x + -2) + 8

Reorder the terms:
8 + 36x + -9x2 = 4(-2 + 3x) + 8
8 + 36x + -9x2 = (-2 * 4 + 3x * 4) + 8
8 + 36x + -9x2 = (-8 + 12x) + 8

Reorder the terms:
8 + 36x + -9x2 = -8 + 8 + 12x

Combine like terms: -8 + 8 = 0
8 + 36x + -9x2 = 0 + 12x
8 + 36x + -9x2 = 12x

Solving
8 + 36x + -9x2 = 12x

Solving for variable 'x'.

Reorder the terms:
8 + 36x + -12x + -9x2 = 12x + -12x

Combine like terms: 36x + -12x = 24x
8 + 24x + -9x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
8 + 24x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-0.8888888889 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -2.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -2.666666667x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + 0.8888888889
-2.666666667x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-2.666666667x + x2 = 0.8888888889

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 0.8888888889 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 0.8888888889 + 1.777777780

Combine like terms: 0.8888888889 + 1.777777780 = 2.6666666689
1.777777780 + -2.666666667x + x2 = 2.6666666689

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 2.6666666689

Calculate the square root of the right side: 1.632993163

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.632993163 and -1.632993163.

Subproblem 1

x + -1.333333334 = 1.632993163 Simplifying x + -1.333333334 = 1.632993163 Reorder the terms: -1.333333334 + x = 1.632993163 Solving -1.333333334 + x = 1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.632993163 + 1.333333334 x = 1.632993163 + 1.333333334 Combine like terms: 1.632993163 + 1.333333334 = 2.966326497 x = 2.966326497 Simplifying x = 2.966326497

Subproblem 2

x + -1.333333334 = -1.632993163 Simplifying x + -1.333333334 = -1.632993163 Reorder the terms: -1.333333334 + x = -1.632993163 Solving -1.333333334 + x = -1.632993163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.632993163 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.632993163 + 1.333333334 x = -1.632993163 + 1.333333334 Combine like terms: -1.632993163 + 1.333333334 = -0.299659829 x = -0.299659829 Simplifying x = -0.299659829

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.966326497, -0.299659829}

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