(3x+25)2x=180

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Solution for (3x+25)2x=180 equation: 


Simplifying
(3x + 25) * 2x = 180

Reorder the terms:
(25 + 3x) * 2x = 180

Reorder the terms for easier multiplication:
2x(25 + 3x) = 180
(25 * 2x + 3x * 2x) = 180
(50x + 6x2) = 180

Solving
50x + 6x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 50x + 6x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 50x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-90 + 25x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-90 + 25x + 3x2)' equal to zero and attempt to solve:

Simplifying
-90 + 25x + 3x2 = 0

Solving
-90 + 25x + 3x2 = 0

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

Divide each side by '3'.
-30 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 8.333333333x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 8.333333333x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 8.333333333x + x2 = 0 + 30
8.333333333x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
8.333333333x + x2 = 30

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 30 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 30 + 17.36111111

Combine like terms: 30 + 17.36111111 = 47.36111111
17.36111111 + 8.333333333x + x2 = 47.36111111

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 47.36111111

Calculate the square root of the right side: 6.881940941

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 6.881940941 and -6.881940941.


Subproblem 1
x + 4.166666667 = 6.881940941

Simplifying
x + 4.166666667 = 6.881940941

Reorder the terms:
4.166666667 + x = 6.881940941

Solving
4.166666667 + x = 6.881940941

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 6.881940941 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 6.881940941 + -4.166666667
x = 6.881940941 + -4.166666667

Combine like terms: 6.881940941 + -4.166666667 = 2.715274274
x = 2.715274274

Simplifying
x = 2.715274274


Subproblem 2
x + 4.166666667 = -6.881940941

Simplifying
x + 4.166666667 = -6.881940941

Reorder the terms:
4.166666667 + x = -6.881940941

Solving
4.166666667 + x = -6.881940941

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -6.881940941 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -6.881940941 + -4.166666667
x = -6.881940941 + -4.166666667

Combine like terms: -6.881940941 + -4.166666667 = -11.048607608
x = -11.048607608

Simplifying
x = -11.048607608


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.715274274, -11.048607608}
Solution
x = {2.715274274, -11.048607608}

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