3x(x+20)+44=18

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Solution for 3x(x+20)+44=18 equation: 


Simplifying
3x(x + 20) + 44 = 18

Reorder the terms:
3x(20 + x) + 44 = 18
(20 * 3x + x * 3x) + 44 = 18
(60x + 3x2) + 44 = 18

Reorder the terms:
44 + 60x + 3x2 = 18

Solving
44 + 60x + 3x2 = 18

Solving for variable 'x'.

Reorder the terms:
44 + -18 + 60x + 3x2 = 18 + -18

Combine like terms: 44 + -18 = 26
26 + 60x + 3x2 = 18 + -18

Combine like terms: 18 + -18 = 0
26 + 60x + 3x2 = 0

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

Divide each side by '3'.
8.666666667 + 20x + x2 = 0

Move the constant term to the right:

Add '-8.666666667' to each side of the equation.
8.666666667 + 20x + -8.666666667 + x2 = 0 + -8.666666667

Reorder the terms:
8.666666667 + -8.666666667 + 20x + x2 = 0 + -8.666666667

Combine like terms: 8.666666667 + -8.666666667 = 0.000000000
0.000000000 + 20x + x2 = 0 + -8.666666667
20x + x2 = 0 + -8.666666667

Combine like terms: 0 + -8.666666667 = -8.666666667
20x + x2 = -8.666666667

The x term is 20x.  Take half its coefficient (10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
20x + 100 + x2 = -8.666666667 + 100

Reorder the terms:
100 + 20x + x2 = -8.666666667 + 100

Combine like terms: -8.666666667 + 100 = 91.333333333
100 + 20x + x2 = 91.333333333

Factor a perfect square on the left side:
(x + 10)(x + 10) = 91.333333333

Calculate the square root of the right side: 9.556847458

Break this problem into two subproblems by setting 
(x + 10) equal to 9.556847458 and -9.556847458.


Subproblem 1
x + 10 = 9.556847458

Simplifying
x + 10 = 9.556847458

Reorder the terms:
10 + x = 9.556847458

Solving
10 + x = 9.556847458

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = 9.556847458 + -10

Combine like terms: 10 + -10 = 0
0 + x = 9.556847458 + -10
x = 9.556847458 + -10

Combine like terms: 9.556847458 + -10 = -0.443152542
x = -0.443152542

Simplifying
x = -0.443152542


Subproblem 2
x + 10 = -9.556847458

Simplifying
x + 10 = -9.556847458

Reorder the terms:
10 + x = -9.556847458

Solving
10 + x = -9.556847458

Solving for variable 'x'.

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

Add '-10' to each side of the equation.
10 + -10 + x = -9.556847458 + -10

Combine like terms: 10 + -10 = 0
0 + x = -9.556847458 + -10
x = -9.556847458 + -10

Combine like terms: -9.556847458 + -10 = -19.556847458
x = -19.556847458

Simplifying
x = -19.556847458


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.443152542, -19.556847458}

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