2x(3x+4)=16x+5x+27

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Solution for 2x(3x+4)=16x+5x+27 equation:


Simplifying
2x(3x + 4) = 16x + 5x + 27

Reorder the terms:
2x(4 + 3x) = 16x + 5x + 27
(4 * 2x + 3x * 2x) = 16x + 5x + 27
(8x + 6x2) = 16x + 5x + 27

Reorder the terms:
8x + 6x2 = 27 + 16x + 5x

Combine like terms: 16x + 5x = 21x
8x + 6x2 = 27 + 21x

Solving
8x + 6x2 = 27 + 21x

Solving for variable 'x'.

Reorder the terms:
-27 + 8x + -21x + 6x2 = 27 + 21x + -27 + -21x

Combine like terms: 8x + -21x = -13x
-27 + -13x + 6x2 = 27 + 21x + -27 + -21x

Reorder the terms:
-27 + -13x + 6x2 = 27 + -27 + 21x + -21x

Combine like terms: 27 + -27 = 0
-27 + -13x + 6x2 = 0 + 21x + -21x
-27 + -13x + 6x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-27 + -13x + 6x2 = 0

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

Divide each side by '6'.
-4.5 + -2.166666667x + x2 = 0

Move the constant term to the right:

Add '4.5' to each side of the equation.
-4.5 + -2.166666667x + 4.5 + x2 = 0 + 4.5

Reorder the terms:
-4.5 + 4.5 + -2.166666667x + x2 = 0 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + -2.166666667x + x2 = 0 + 4.5
-2.166666667x + x2 = 0 + 4.5

Combine like terms: 0 + 4.5 = 4.5
-2.166666667x + x2 = 4.5

The x term is -2.166666667x.  Take half its coefficient (-1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
-2.166666667x + 1.173611113 + x2 = 4.5 + 1.173611113

Reorder the terms:
1.173611113 + -2.166666667x + x2 = 4.5 + 1.173611113

Combine like terms: 4.5 + 1.173611113 = 5.673611113
1.173611113 + -2.166666667x + x2 = 5.673611113

Factor a perfect square on the left side:
(x + -1.083333334)(x + -1.083333334) = 5.673611113

Calculate the square root of the right side: 2.381934322

Break this problem into two subproblems by setting 
(x + -1.083333334) equal to 2.381934322 and -2.381934322.

Subproblem 1

x + -1.083333334 = 2.381934322 Simplifying x + -1.083333334 = 2.381934322 Reorder the terms: -1.083333334 + x = 2.381934322 Solving -1.083333334 + x = 2.381934322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 2.381934322 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 2.381934322 + 1.083333334 x = 2.381934322 + 1.083333334 Combine like terms: 2.381934322 + 1.083333334 = 3.465267656 x = 3.465267656 Simplifying x = 3.465267656

Subproblem 2

x + -1.083333334 = -2.381934322 Simplifying x + -1.083333334 = -2.381934322 Reorder the terms: -1.083333334 + x = -2.381934322 Solving -1.083333334 + x = -2.381934322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -2.381934322 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -2.381934322 + 1.083333334 x = -2.381934322 + 1.083333334 Combine like terms: -2.381934322 + 1.083333334 = -1.298600988 x = -1.298600988 Simplifying x = -1.298600988

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.465267656, -1.298600988}

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