2x(3x+1)=36x+5

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Solution for 2x(3x+1)=36x+5 equation:


Simplifying
2x(3x + 1) = 36x + 5

Reorder the terms:
2x(1 + 3x) = 36x + 5
(1 * 2x + 3x * 2x) = 36x + 5
(2x + 6x2) = 36x + 5

Reorder the terms:
2x + 6x2 = 5 + 36x

Solving
2x + 6x2 = 5 + 36x

Solving for variable 'x'.

Reorder the terms:
-5 + 2x + -36x + 6x2 = 5 + 36x + -5 + -36x

Combine like terms: 2x + -36x = -34x
-5 + -34x + 6x2 = 5 + 36x + -5 + -36x

Reorder the terms:
-5 + -34x + 6x2 = 5 + -5 + 36x + -36x

Combine like terms: 5 + -5 = 0
-5 + -34x + 6x2 = 0 + 36x + -36x
-5 + -34x + 6x2 = 36x + -36x

Combine like terms: 36x + -36x = 0
-5 + -34x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + -5.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -5.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -5.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -5.666666667x + x2 = 0 + 0.8333333333
-5.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-5.666666667x + x2 = 0.8333333333

The x term is -5.666666667x.  Take half its coefficient (-2.833333334).
Square it (8.027777782) and add it to both sides.

Add '8.027777782' to each side of the equation.
-5.666666667x + 8.027777782 + x2 = 0.8333333333 + 8.027777782

Reorder the terms:
8.027777782 + -5.666666667x + x2 = 0.8333333333 + 8.027777782

Combine like terms: 0.8333333333 + 8.027777782 = 8.8611111153
8.027777782 + -5.666666667x + x2 = 8.8611111153

Factor a perfect square on the left side:
(x + -2.833333334)(x + -2.833333334) = 8.8611111153

Calculate the square root of the right side: 2.976761851

Break this problem into two subproblems by setting 
(x + -2.833333334) equal to 2.976761851 and -2.976761851.

Subproblem 1

x + -2.833333334 = 2.976761851 Simplifying x + -2.833333334 = 2.976761851 Reorder the terms: -2.833333334 + x = 2.976761851 Solving -2.833333334 + x = 2.976761851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = 2.976761851 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = 2.976761851 + 2.833333334 x = 2.976761851 + 2.833333334 Combine like terms: 2.976761851 + 2.833333334 = 5.810095185 x = 5.810095185 Simplifying x = 5.810095185

Subproblem 2

x + -2.833333334 = -2.976761851 Simplifying x + -2.833333334 = -2.976761851 Reorder the terms: -2.833333334 + x = -2.976761851 Solving -2.833333334 + x = -2.976761851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.833333334' to each side of the equation. -2.833333334 + 2.833333334 + x = -2.976761851 + 2.833333334 Combine like terms: -2.833333334 + 2.833333334 = 0.000000000 0.000000000 + x = -2.976761851 + 2.833333334 x = -2.976761851 + 2.833333334 Combine like terms: -2.976761851 + 2.833333334 = -0.143428517 x = -0.143428517 Simplifying x = -0.143428517

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.810095185, -0.143428517}

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