2(x-5).5(x-4)=5

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Solution for 2(x-5).5(x-4)=5 equation: 


Simplifying
2(x + -5) * 0.5(x + -4) = 5

Reorder the terms:
2(-5 + x) * 0.5(x + -4) = 5

Reorder the terms:
2(-5 + x) * 0.5(-4 + x) = 5

Reorder the terms for easier multiplication:
2 * 0.5(-5 + x)(-4 + x) = 5

Multiply 2 * 0.5
1(-5 + x)(-4 + x) = 5

Multiply (-5 + x) * (-4 + x)
1(-5(-4 + x) + x(-4 + x)) = 5
1((-4 * -5 + x * -5) + x(-4 + x)) = 5
1((20 + -5x) + x(-4 + x)) = 5
1(20 + -5x + (-4 * x + x * x)) = 5
1(20 + -5x + (-4x + x2)) = 5

Combine like terms: -5x + -4x = -9x
1(20 + -9x + x2) = 5
(20 * 1 + -9x * 1 + x2 * 1) = 5
(20 + -9x + 1x2) = 5

Solving
20 + -9x + 1x2 = 5

Solving for variable 'x'.

Reorder the terms:
20 + -5 + -9x + 1x2 = 5 + -5

Combine like terms: 20 + -5 = 15
15 + -9x + 1x2 = 5 + -5

Combine like terms: 5 + -5 = 0
15 + -9x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -9x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -9x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -9x + x2 = 0 + -15
-9x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-9x + x2 = -15

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -15 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -15 + 20.25

Combine like terms: -15 + 20.25 = 5.25
20.25 + -9x + x2 = 5.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + -4.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + -4.5 = 2.291287847

Simplifying
x + -4.5 = 2.291287847

Reorder the terms:
-4.5 + x = 2.291287847

Solving
-4.5 + x = 2.291287847

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 2.291287847 + 4.5
x = 2.291287847 + 4.5

Combine like terms: 2.291287847 + 4.5 = 6.791287847
x = 6.791287847

Simplifying
x = 6.791287847


Subproblem 2
x + -4.5 = -2.291287847

Simplifying
x + -4.5 = -2.291287847

Reorder the terms:
-4.5 + x = -2.291287847

Solving
-4.5 + x = -2.291287847

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -2.291287847 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -2.291287847 + 4.5
x = -2.291287847 + 4.5

Combine like terms: -2.291287847 + 4.5 = 2.208712153
x = 2.208712153

Simplifying
x = 2.208712153


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.791287847, 2.208712153}

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