2x(x+25)=90

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Solution for 2x(x+25)=90 equation: 


Simplifying
2x(x + 25) = 90

Reorder the terms:
2x(25 + x) = 90
(25 * 2x + x * 2x) = 90
(50x + 2x2) = 90

Solving
50x + 2x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 50x + 2x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 50x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 25x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 25x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 25x + x2 = 0

Solving
-45 + 25x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 25x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 25x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 25x + x2 = 0 + 45
25x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
25x + x2 = 45

The x term is 25x.  Take half its coefficient (12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
25x + 156.25 + x2 = 45 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 45 + 156.25

Combine like terms: 45 + 156.25 = 201.25
156.25 + 25x + x2 = 201.25

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 201.25

Calculate the square root of the right side: 14.186260959

Break this problem into two subproblems by setting 
(x + 12.5) equal to 14.186260959 and -14.186260959.


Subproblem 1
x + 12.5 = 14.186260959

Simplifying
x + 12.5 = 14.186260959

Reorder the terms:
12.5 + x = 14.186260959

Solving
12.5 + x = 14.186260959

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = 14.186260959 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 14.186260959 + -12.5
x = 14.186260959 + -12.5

Combine like terms: 14.186260959 + -12.5 = 1.686260959
x = 1.686260959

Simplifying
x = 1.686260959


Subproblem 2
x + 12.5 = -14.186260959

Simplifying
x + 12.5 = -14.186260959

Reorder the terms:
12.5 + x = -14.186260959

Solving
12.5 + x = -14.186260959

Solving for variable 'x'.

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

Add '-12.5' to each side of the equation.
12.5 + -12.5 + x = -14.186260959 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -14.186260959 + -12.5
x = -14.186260959 + -12.5

Combine like terms: -14.186260959 + -12.5 = -26.686260959
x = -26.686260959

Simplifying
x = -26.686260959


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.686260959, -26.686260959}
Solution
x = {1.686260959, -26.686260959}

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