4x(x+25)=90

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Solution for 4x(x+25)=90 equation: 


Simplifying
4x(x + 25) = 90

Reorder the terms:
4x(25 + x) = 90
(25 * 4x + x * 4x) = 90
(100x + 4x2) = 90

Solving
100x + 4x2 = 90

Solving for variable 'x'.

Reorder the terms:
-90 + 100x + 4x2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + 100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + 50x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 50x + 2x2)' equal to zero and attempt to solve:

Simplifying
-45 + 50x + 2x2 = 0

Solving
-45 + 50x + 2x2 = 0

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

Divide each side by '2'.
-22.5 + 25x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 25x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 25x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 25x + x2 = 0 + 22.5
25x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
25x + x2 = 22.5

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 = 22.5 + 156.25

Reorder the terms:
156.25 + 25x + x2 = 22.5 + 156.25

Combine like terms: 22.5 + 156.25 = 178.75
156.25 + 25x + x2 = 178.75

Factor a perfect square on the left side:
(x + 12.5)(x + 12.5) = 178.75

Calculate the square root of the right side: 13.369741957

Break this problem into two subproblems by setting 
(x + 12.5) equal to 13.369741957 and -13.369741957.


Subproblem 1
x + 12.5 = 13.369741957

Simplifying
x + 12.5 = 13.369741957

Reorder the terms:
12.5 + x = 13.369741957

Solving
12.5 + x = 13.369741957

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 = 13.369741957 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = 13.369741957 + -12.5
x = 13.369741957 + -12.5

Combine like terms: 13.369741957 + -12.5 = 0.869741957
x = 0.869741957

Simplifying
x = 0.869741957


Subproblem 2
x + 12.5 = -13.369741957

Simplifying
x + 12.5 = -13.369741957

Reorder the terms:
12.5 + x = -13.369741957

Solving
12.5 + x = -13.369741957

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 = -13.369741957 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + x = -13.369741957 + -12.5
x = -13.369741957 + -12.5

Combine like terms: -13.369741957 + -12.5 = -25.869741957
x = -25.869741957

Simplifying
x = -25.869741957


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.869741957, -25.869741957}
Solution
x = {0.869741957, -25.869741957}

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