3x(5+x)=29+x

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Solution for 3x(5+x)=29+x equation:


Simplifying
3x(5 + x) = 29 + x
(5 * 3x + x * 3x) = 29 + x
(15x + 3x2) = 29 + x

Solving
15x + 3x2 = 29 + x

Solving for variable 'x'.

Reorder the terms:
-29 + 15x + -1x + 3x2 = 29 + x + -29 + -1x

Combine like terms: 15x + -1x = 14x
-29 + 14x + 3x2 = 29 + x + -29 + -1x

Reorder the terms:
-29 + 14x + 3x2 = 29 + -29 + x + -1x

Combine like terms: 29 + -29 = 0
-29 + 14x + 3x2 = 0 + x + -1x
-29 + 14x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
-29 + 14x + 3x2 = 0

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

Divide each side by '3'.
-9.666666667 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '9.666666667' to each side of the equation.
-9.666666667 + 4.666666667x + 9.666666667 + x2 = 0 + 9.666666667

Reorder the terms:
-9.666666667 + 9.666666667 + 4.666666667x + x2 = 0 + 9.666666667

Combine like terms: -9.666666667 + 9.666666667 = 0.000000000
0.000000000 + 4.666666667x + x2 = 0 + 9.666666667
4.666666667x + x2 = 0 + 9.666666667

Combine like terms: 0 + 9.666666667 = 9.666666667
4.666666667x + x2 = 9.666666667

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 9.666666667 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 9.666666667 + 5.444444448

Combine like terms: 9.666666667 + 5.444444448 = 15.111111115
5.444444448 + 4.666666667x + x2 = 15.111111115

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 15.111111115

Calculate the square root of the right side: 3.887301264

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 3.887301264 and -3.887301264.

Subproblem 1

x + 2.333333334 = 3.887301264 Simplifying x + 2.333333334 = 3.887301264 Reorder the terms: 2.333333334 + x = 3.887301264 Solving 2.333333334 + x = 3.887301264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = 3.887301264 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = 3.887301264 + -2.333333334 x = 3.887301264 + -2.333333334 Combine like terms: 3.887301264 + -2.333333334 = 1.55396793 x = 1.55396793 Simplifying x = 1.55396793

Subproblem 2

x + 2.333333334 = -3.887301264 Simplifying x + 2.333333334 = -3.887301264 Reorder the terms: 2.333333334 + x = -3.887301264 Solving 2.333333334 + x = -3.887301264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.333333334' to each side of the equation. 2.333333334 + -2.333333334 + x = -3.887301264 + -2.333333334 Combine like terms: 2.333333334 + -2.333333334 = 0.000000000 0.000000000 + x = -3.887301264 + -2.333333334 x = -3.887301264 + -2.333333334 Combine like terms: -3.887301264 + -2.333333334 = -6.220634598 x = -6.220634598 Simplifying x = -6.220634598

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.55396793, -6.220634598}

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