2x+3x(x-10)=45

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Solution for 2x+3x(x-10)=45 equation: 


Simplifying
2x + 3x(x + -10) = 45

Reorder the terms:
2x + 3x(-10 + x) = 45
2x + (-10 * 3x + x * 3x) = 45
2x + (-30x + 3x2) = 45

Combine like terms: 2x + -30x = -28x
-28x + 3x2 = 45

Solving
-28x + 3x2 = 45

Solving for variable 'x'.

Reorder the terms:
-45 + -28x + 3x2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + -28x + 3x2 = 0

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

Divide each side by '3'.
-15 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -9.333333333x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -9.333333333x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -9.333333333x + x2 = 0 + 15
-9.333333333x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-9.333333333x + x2 = 15

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 15 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 15 + 21.77777778

Combine like terms: 15 + 21.77777778 = 36.77777778
21.77777778 + -9.333333333x + x2 = 36.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 36.77777778

Calculate the square root of the right side: 6.064468466

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 6.064468466 and -6.064468466.


Subproblem 1
x + -4.666666667 = 6.064468466

Simplifying
x + -4.666666667 = 6.064468466

Reorder the terms:
-4.666666667 + x = 6.064468466

Solving
-4.666666667 + x = 6.064468466

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 6.064468466 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 6.064468466 + 4.666666667
x = 6.064468466 + 4.666666667

Combine like terms: 6.064468466 + 4.666666667 = 10.731135133
x = 10.731135133

Simplifying
x = 10.731135133


Subproblem 2
x + -4.666666667 = -6.064468466

Simplifying
x + -4.666666667 = -6.064468466

Reorder the terms:
-4.666666667 + x = -6.064468466

Solving
-4.666666667 + x = -6.064468466

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -6.064468466 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -6.064468466 + 4.666666667
x = -6.064468466 + 4.666666667

Combine like terms: -6.064468466 + 4.666666667 = -1.397801799
x = -1.397801799

Simplifying
x = -1.397801799


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.731135133, -1.397801799}

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