(3x+8)(x+8)-832=

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Solution for (3x+8)(x+8)-832= equation:


Simplifying
(3x + 8)(x + 8) + -832 = 0

Reorder the terms:
(8 + 3x)(x + 8) + -832 = 0

Reorder the terms:
(8 + 3x)(8 + x) + -832 = 0

Multiply (8 + 3x) * (8 + x)
(8(8 + x) + 3x * (8 + x)) + -832 = 0
((8 * 8 + x * 8) + 3x * (8 + x)) + -832 = 0
((64 + 8x) + 3x * (8 + x)) + -832 = 0
(64 + 8x + (8 * 3x + x * 3x)) + -832 = 0
(64 + 8x + (24x + 3x2)) + -832 = 0

Combine like terms: 8x + 24x = 32x
(64 + 32x + 3x2) + -832 = 0

Reorder the terms:
64 + -832 + 32x + 3x2 = 0

Combine like terms: 64 + -832 = -768
-768 + 32x + 3x2 = 0

Solving
-768 + 32x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-256 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '256' to each side of the equation.
-256 + 10.66666667x + 256 + x2 = 0 + 256

Reorder the terms:
-256 + 256 + 10.66666667x + x2 = 0 + 256

Combine like terms: -256 + 256 = 0
0 + 10.66666667x + x2 = 0 + 256
10.66666667x + x2 = 0 + 256

Combine like terms: 0 + 256 = 256
10.66666667x + x2 = 256

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = 256 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = 256 + 28.44444446

Combine like terms: 256 + 28.44444446 = 284.44444446
28.44444446 + 10.66666667x + x2 = 284.44444446

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = 284.44444446

Calculate the square root of the right side: 16.865480855

Break this problem into two subproblems by setting 
(x + 5.333333335) equal to 16.865480855 and -16.865480855.

Subproblem 1

x + 5.333333335 = 16.865480855 Simplifying x + 5.333333335 = 16.865480855 Reorder the terms: 5.333333335 + x = 16.865480855 Solving 5.333333335 + x = 16.865480855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = 16.865480855 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = 16.865480855 + -5.333333335 x = 16.865480855 + -5.333333335 Combine like terms: 16.865480855 + -5.333333335 = 11.53214752 x = 11.53214752 Simplifying x = 11.53214752

Subproblem 2

x + 5.333333335 = -16.865480855 Simplifying x + 5.333333335 = -16.865480855 Reorder the terms: 5.333333335 + x = -16.865480855 Solving 5.333333335 + x = -16.865480855 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + x = -16.865480855 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + x = -16.865480855 + -5.333333335 x = -16.865480855 + -5.333333335 Combine like terms: -16.865480855 + -5.333333335 = -22.19881419 x = -22.19881419 Simplifying x = -22.19881419

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.53214752, -22.19881419}

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