(4X+10)5X=80

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Solution for (4X+10)5X=80 equation: 


Simplifying
(4X + 10) * 5X = 80

Reorder the terms:
(10 + 4X) * 5X = 80

Reorder the terms for easier multiplication:
5X(10 + 4X) = 80
(10 * 5X + 4X * 5X) = 80
(50X + 20X2) = 80

Solving
50X + 20X2 = 80

Solving for variable 'X'.

Reorder the terms:
-80 + 50X + 20X2 = 80 + -80

Combine like terms: 80 + -80 = 0
-80 + 50X + 20X2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-8 + 5X + 2X2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-8 + 5X + 2X2)' equal to zero and attempt to solve:

Simplifying
-8 + 5X + 2X2 = 0

Solving
-8 + 5X + 2X2 = 0

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

Divide each side by '2'.
-4 + 2.5X + X2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 2.5X + 4 + X2 = 0 + 4

Reorder the terms:
-4 + 4 + 2.5X + X2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 2.5X + X2 = 0 + 4
2.5X + X2 = 0 + 4

Combine like terms: 0 + 4 = 4
2.5X + X2 = 4

The X term is 2.5X.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5X + 1.5625 + X2 = 4 + 1.5625

Reorder the terms:
1.5625 + 2.5X + X2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + 2.5X + X2 = 5.5625

Factor a perfect square on the left side:
(X + 1.25)(X + 1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(X + 1.25) equal to 2.358495283 and -2.358495283.


Subproblem 1
X + 1.25 = 2.358495283

Simplifying
X + 1.25 = 2.358495283

Reorder the terms:
1.25 + X = 2.358495283

Solving
1.25 + X = 2.358495283

Solving for variable 'X'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + X = 2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + X = 2.358495283 + -1.25
X = 2.358495283 + -1.25

Combine like terms: 2.358495283 + -1.25 = 1.108495283
X = 1.108495283

Simplifying
X = 1.108495283


Subproblem 2
X + 1.25 = -2.358495283

Simplifying
X + 1.25 = -2.358495283

Reorder the terms:
1.25 + X = -2.358495283

Solving
1.25 + X = -2.358495283

Solving for variable 'X'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + X = -2.358495283 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + X = -2.358495283 + -1.25
X = -2.358495283 + -1.25

Combine like terms: -2.358495283 + -1.25 = -3.608495283
X = -3.608495283

Simplifying
X = -3.608495283


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.108495283, -3.608495283}
Solution
X = {1.108495283, -3.608495283}

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