2x(3x+5)=49

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Solution for 2x(3x+5)=49 equation: 


Simplifying
2x(3x + 5) = 49

Reorder the terms:
2x(5 + 3x) = 49
(5 * 2x + 3x * 2x) = 49
(10x + 6x2) = 49

Solving
10x + 6x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + 10x + 6x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 10x + 6x2 = 0

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

Divide each side by '6'.
-8.166666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '8.166666667' to each side of the equation.
-8.166666667 + 1.666666667x + 8.166666667 + x2 = 0 + 8.166666667

Reorder the terms:
-8.166666667 + 8.166666667 + 1.666666667x + x2 = 0 + 8.166666667

Combine like terms: -8.166666667 + 8.166666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + 8.166666667
1.666666667x + x2 = 0 + 8.166666667

Combine like terms: 0 + 8.166666667 = 8.166666667
1.666666667x + x2 = 8.166666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 8.166666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 8.166666667 + 0.6944444447

Combine like terms: 8.166666667 + 0.6944444447 = 8.8611111117
0.6944444447 + 1.666666667x + x2 = 8.8611111117

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 8.8611111117

Calculate the square root of the right side: 2.97676185

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 2.97676185 and -2.97676185.


Subproblem 1
x + 0.8333333335 = 2.97676185

Simplifying
x + 0.8333333335 = 2.97676185

Reorder the terms:
0.8333333335 + x = 2.97676185

Solving
0.8333333335 + x = 2.97676185

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 2.97676185 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 2.97676185 + -0.8333333335
x = 2.97676185 + -0.8333333335

Combine like terms: 2.97676185 + -0.8333333335 = 2.1434285165
x = 2.1434285165

Simplifying
x = 2.1434285165


Subproblem 2
x + 0.8333333335 = -2.97676185

Simplifying
x + 0.8333333335 = -2.97676185

Reorder the terms:
0.8333333335 + x = -2.97676185

Solving
0.8333333335 + x = -2.97676185

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -2.97676185 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -2.97676185 + -0.8333333335
x = -2.97676185 + -0.8333333335

Combine like terms: -2.97676185 + -0.8333333335 = -3.8100951835
x = -3.8100951835

Simplifying
x = -3.8100951835


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.1434285165, -3.8100951835}

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