(4.77(X-80))(.808(X-25))=0

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Solution for (4.77(X-80))(.808(X-25))=0 equation:


Simplifying
(4.77(X + -80))(0.808(X + -25)) = 0

Reorder the terms:
(4.77(-80 + X))(0.808(X + -25)) = 0
((-80 * 4.77 + X * 4.77))(0.808(X + -25)) = 0
((-381.6 + 4.77X))(0.808(X + -25)) = 0

Reorder the terms:
(-381.6 + 4.77X)(0.808(-25 + X)) = 0
(-381.6 + 4.77X)((-25 * 0.808 + X * 0.808)) = 0
(-381.6 + 4.77X)((-20.2 + 0.808X)) = 0

Multiply (-381.6 + 4.77X) * (-20.2 + 0.808X)
(-381.6(-20.2 + 0.808X) + 4.77X * (-20.2 + 0.808X)) = 0
((-20.2 * -381.6 + 0.808X * -381.6) + 4.77X * (-20.2 + 0.808X)) = 0
((7708.32 + -308.3328X) + 4.77X * (-20.2 + 0.808X)) = 0
(7708.32 + -308.3328X + (-20.2 * 4.77X + 0.808X * 4.77X)) = 0
(7708.32 + -308.3328X + (-96.354X + 3.85416X2)) = 0

Combine like terms: -308.3328X + -96.354X = -404.6868X
(7708.32 + -404.6868X + 3.85416X2) = 0

Solving
7708.32 + -404.6868X + 3.85416X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
3.85416 the coefficient of the squared term: 

Divide each side by '3.85416'.
2000 + -105X + X2 = 0

Move the constant term to the right:

Add '-2000' to each side of the equation.
2000 + -105X + -2000 + X2 = 0 + -2000

Reorder the terms:
2000 + -2000 + -105X + X2 = 0 + -2000

Combine like terms: 2000 + -2000 = 0
0 + -105X + X2 = 0 + -2000
-105X + X2 = 0 + -2000

Combine like terms: 0 + -2000 = -2000
-105X + X2 = -2000

The X term is -105X.  Take half its coefficient (-52.5).
Square it (2756.25) and add it to both sides.

Add '2756.25' to each side of the equation.
-105X + 2756.25 + X2 = -2000 + 2756.25

Reorder the terms:
2756.25 + -105X + X2 = -2000 + 2756.25

Combine like terms: -2000 + 2756.25 = 756.25
2756.25 + -105X + X2 = 756.25

Factor a perfect square on the left side:
(X + -52.5)(X + -52.5) = 756.25

Calculate the square root of the right side: 27.5

Break this problem into two subproblems by setting 
(X + -52.5) equal to 27.5 and -27.5.

Subproblem 1

X + -52.5 = 27.5 Simplifying X + -52.5 = 27.5 Reorder the terms: -52.5 + X = 27.5 Solving -52.5 + X = 27.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + X = 27.5 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + X = 27.5 + 52.5 X = 27.5 + 52.5 Combine like terms: 27.5 + 52.5 = 80 X = 80 Simplifying X = 80

Subproblem 2

X + -52.5 = -27.5 Simplifying X + -52.5 = -27.5 Reorder the terms: -52.5 + X = -27.5 Solving -52.5 + X = -27.5 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '52.5' to each side of the equation. -52.5 + 52.5 + X = -27.5 + 52.5 Combine like terms: -52.5 + 52.5 = 0.0 0.0 + X = -27.5 + 52.5 X = -27.5 + 52.5 Combine like terms: -27.5 + 52.5 = 25 X = 25 Simplifying X = 25

Solution

The solution to the problem is based on the solutions from the subproblems. X = {80, 25}

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