3x(x+50)+90=180

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Solution for 3x(x+50)+90=180 equation: 


Simplifying
3x(x + 50) + 90 = 180

Reorder the terms:
3x(50 + x) + 90 = 180
(50 * 3x + x * 3x) + 90 = 180
(150x + 3x2) + 90 = 180

Reorder the terms:
90 + 150x + 3x2 = 180

Solving
90 + 150x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
90 + -180 + 150x + 3x2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + 150x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + 150x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 50x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-30 + 50x + x2)' equal to zero and attempt to solve:

Simplifying
-30 + 50x + x2 = 0

Solving
-30 + 50x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 50x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 50x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 50x + x2 = 0 + 30
50x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
50x + x2 = 30

The x term is 50x.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50x + 625 + x2 = 30 + 625

Reorder the terms:
625 + 50x + x2 = 30 + 625

Combine like terms: 30 + 625 = 655
625 + 50x + x2 = 655

Factor a perfect square on the left side:
(x + 25)(x + 25) = 655

Calculate the square root of the right side: 25.592967784

Break this problem into two subproblems by setting 
(x + 25) equal to 25.592967784 and -25.592967784.


Subproblem 1
x + 25 = 25.592967784

Simplifying
x + 25 = 25.592967784

Reorder the terms:
25 + x = 25.592967784

Solving
25 + x = 25.592967784

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = 25.592967784 + -25

Combine like terms: 25 + -25 = 0
0 + x = 25.592967784 + -25
x = 25.592967784 + -25

Combine like terms: 25.592967784 + -25 = 0.592967784
x = 0.592967784

Simplifying
x = 0.592967784


Subproblem 2
x + 25 = -25.592967784

Simplifying
x + 25 = -25.592967784

Reorder the terms:
25 + x = -25.592967784

Solving
25 + x = -25.592967784

Solving for variable 'x'.

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

Add '-25' to each side of the equation.
25 + -25 + x = -25.592967784 + -25

Combine like terms: 25 + -25 = 0
0 + x = -25.592967784 + -25
x = -25.592967784 + -25

Combine like terms: -25.592967784 + -25 = -50.592967784
x = -50.592967784

Simplifying
x = -50.592967784


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.592967784, -50.592967784}
Solution
x = {0.592967784, -50.592967784}

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