(x+20)3x+44=180

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Solution for (x+20)3x+44=180 equation:


Simplifying
(x + 20) * 3x + 44 = 180

Reorder the terms:
(20 + x) * 3x + 44 = 180

Reorder the terms for easier multiplication:
3x(20 + x) + 44 = 180
(20 * 3x + x * 3x) + 44 = 180
(60x + 3x2) + 44 = 180

Reorder the terms:
44 + 60x + 3x2 = 180

Solving
44 + 60x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
44 + -180 + 60x + 3x2 = 180 + -180

Combine like terms: 44 + -180 = -136
-136 + 60x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-136 + 60x + 3x2 = 0

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

Divide each side by '3'.
-45.33333333 + 20x + x2 = 0

Move the constant term to the right:

Add '45.33333333' to each side of the equation.
-45.33333333 + 20x + 45.33333333 + x2 = 0 + 45.33333333

Reorder the terms:
-45.33333333 + 45.33333333 + 20x + x2 = 0 + 45.33333333

Combine like terms: -45.33333333 + 45.33333333 = 0.00000000
0.00000000 + 20x + x2 = 0 + 45.33333333
20x + x2 = 0 + 45.33333333

Combine like terms: 0 + 45.33333333 = 45.33333333
20x + x2 = 45.33333333

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 = 45.33333333 + 100

Reorder the terms:
100 + 20x + x2 = 45.33333333 + 100

Combine like terms: 45.33333333 + 100 = 145.33333333
100 + 20x + x2 = 145.33333333

Factor a perfect square on the left side:
(x + 10)(x + 10) = 145.33333333

Calculate the square root of the right side: 12.055427547

Break this problem into two subproblems by setting 
(x + 10) equal to 12.055427547 and -12.055427547.

Subproblem 1

x + 10 = 12.055427547 Simplifying x + 10 = 12.055427547 Reorder the terms: 10 + x = 12.055427547 Solving 10 + x = 12.055427547 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 = 12.055427547 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.055427547 + -10 x = 12.055427547 + -10 Combine like terms: 12.055427547 + -10 = 2.055427547 x = 2.055427547 Simplifying x = 2.055427547

Subproblem 2

x + 10 = -12.055427547 Simplifying x + 10 = -12.055427547 Reorder the terms: 10 + x = -12.055427547 Solving 10 + x = -12.055427547 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 = -12.055427547 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.055427547 + -10 x = -12.055427547 + -10 Combine like terms: -12.055427547 + -10 = -22.055427547 x = -22.055427547 Simplifying x = -22.055427547

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.055427547, -22.055427547}

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