X(4X-20)=90

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Solution for X(4X-20)=90 equation: 


Simplifying
X(4X + -20) = 90

Reorder the terms:
X(-20 + 4X) = 90
(-20 * X + 4X * X) = 90
(-20X + 4X2) = 90

Solving
-20X + 4X2 = 90

Solving for variable 'X'.

Reorder the terms:
-90 + -20X + 4X2 = 90 + -90

Combine like terms: 90 + -90 = 0
-90 + -20X + 4X2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -10X + 2X2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + -10X + 2X2)' equal to zero and attempt to solve:

Simplifying
-45 + -10X + 2X2 = 0

Solving
-45 + -10X + 2X2 = 0

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

Divide each side by '2'.
-22.5 + -5X + X2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + -5X + 22.5 + X2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + -5X + X2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + -5X + X2 = 0 + 22.5
-5X + X2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
-5X + X2 = 22.5

The X term is -5X.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5X + 6.25 + X2 = 22.5 + 6.25

Reorder the terms:
6.25 + -5X + X2 = 22.5 + 6.25

Combine like terms: 22.5 + 6.25 = 28.75
6.25 + -5X + X2 = 28.75

Factor a perfect square on the left side:
(X + -2.5)(X + -2.5) = 28.75

Calculate the square root of the right side: 5.361902647

Break this problem into two subproblems by setting 
(X + -2.5) equal to 5.361902647 and -5.361902647.


Subproblem 1
X + -2.5 = 5.361902647

Simplifying
X + -2.5 = 5.361902647

Reorder the terms:
-2.5 + X = 5.361902647

Solving
-2.5 + X = 5.361902647

Solving for variable 'X'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + X = 5.361902647 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = 5.361902647 + 2.5
X = 5.361902647 + 2.5

Combine like terms: 5.361902647 + 2.5 = 7.861902647
X = 7.861902647

Simplifying
X = 7.861902647


Subproblem 2
X + -2.5 = -5.361902647

Simplifying
X + -2.5 = -5.361902647

Reorder the terms:
-2.5 + X = -5.361902647

Solving
-2.5 + X = -5.361902647

Solving for variable 'X'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + X = -5.361902647 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + X = -5.361902647 + 2.5
X = -5.361902647 + 2.5

Combine like terms: -5.361902647 + 2.5 = -2.861902647
X = -2.861902647

Simplifying
X = -2.861902647


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {7.861902647, -2.861902647}
Solution
X = {7.861902647, -2.861902647}

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