(3x-40)x+10+x-18=

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Solution for (3x-40)x+10+x-18= equation: 


Simplifying
(3x + -40) * x + 10 + x + -18 = 0

Reorder the terms:
(-40 + 3x) * x + 10 + x + -18 = 0

Reorder the terms for easier multiplication:
x(-40 + 3x) + 10 + x + -18 = 0
(-40 * x + 3x * x) + 10 + x + -18 = 0
(-40x + 3x2) + 10 + x + -18 = 0

Reorder the terms:
10 + -18 + -40x + x + 3x2 = 0

Combine like terms: 10 + -18 = -8
-8 + -40x + x + 3x2 = 0

Combine like terms: -40x + x = -39x
-8 + -39x + 3x2 = 0

Solving
-8 + -39x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.666666667 + -13x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -13x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -13x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -13x + x2 = 0 + 2.666666667
-13x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-13x + x2 = 2.666666667

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 2.666666667 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 2.666666667 + 42.25

Combine like terms: 2.666666667 + 42.25 = 44.916666667
42.25 + -13x + x2 = 44.916666667

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 44.916666667

Calculate the square root of the right side: 6.701989754

Break this problem into two subproblems by setting 
(x + -6.5) equal to 6.701989754 and -6.701989754.


Subproblem 1
x + -6.5 = 6.701989754

Simplifying
x + -6.5 = 6.701989754

Reorder the terms:
-6.5 + x = 6.701989754

Solving
-6.5 + x = 6.701989754

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 6.701989754 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 6.701989754 + 6.5
x = 6.701989754 + 6.5

Combine like terms: 6.701989754 + 6.5 = 13.201989754
x = 13.201989754

Simplifying
x = 13.201989754


Subproblem 2
x + -6.5 = -6.701989754

Simplifying
x + -6.5 = -6.701989754

Reorder the terms:
-6.5 + x = -6.701989754

Solving
-6.5 + x = -6.701989754

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -6.701989754 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -6.701989754 + 6.5
x = -6.701989754 + 6.5

Combine like terms: -6.701989754 + 6.5 = -0.201989754
x = -0.201989754

Simplifying
x = -0.201989754


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.201989754, -0.201989754}

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