(155x)(x+2*217)=1426

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Solution for (155x)(x+2*217)=1426 equation: 


Simplifying
(155x)(x + 2 * 217) = 1426

Remove parenthesis around (155x)
155x(x + 2 * 217) = 1426

Multiply 2 * 217
155x(x + 434) = 1426

Reorder the terms:
155x(434 + x) = 1426
(434 * 155x + x * 155x) = 1426
(67270x + 155x2) = 1426

Solving
67270x + 155x2 = 1426

Solving for variable 'x'.

Reorder the terms:
-1426 + 67270x + 155x2 = 1426 + -1426

Combine like terms: 1426 + -1426 = 0
-1426 + 67270x + 155x2 = 0

Factor out the Greatest Common Factor (GCF), '31'.
31(-46 + 2170x + 5x2) = 0

Ignore the factor 31.

Subproblem 1
Set the factor '(-46 + 2170x + 5x2)' equal to zero and attempt to solve:

Simplifying
-46 + 2170x + 5x2 = 0

Solving
-46 + 2170x + 5x2 = 0

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

Divide each side by '5'.
-9.2 + 434x + x2 = 0

Move the constant term to the right:

Add '9.2' to each side of the equation.
-9.2 + 434x + 9.2 + x2 = 0 + 9.2

Reorder the terms:
-9.2 + 9.2 + 434x + x2 = 0 + 9.2

Combine like terms: -9.2 + 9.2 = 0.0
0.0 + 434x + x2 = 0 + 9.2
434x + x2 = 0 + 9.2

Combine like terms: 0 + 9.2 = 9.2
434x + x2 = 9.2

The x term is 434x.  Take half its coefficient (217).
Square it (47089) and add it to both sides.

Add '47089' to each side of the equation.
434x + 47089 + x2 = 9.2 + 47089

Reorder the terms:
47089 + 434x + x2 = 9.2 + 47089

Combine like terms: 9.2 + 47089 = 47098.2
47089 + 434x + x2 = 47098.2

Factor a perfect square on the left side:
(x + 217)(x + 217) = 47098.2

Calculate the square root of the right side: 217.021197121

Break this problem into two subproblems by setting 
(x + 217) equal to 217.021197121 and -217.021197121.


Subproblem 1
x + 217 = 217.021197121

Simplifying
x + 217 = 217.021197121

Reorder the terms:
217 + x = 217.021197121

Solving
217 + x = 217.021197121

Solving for variable 'x'.

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

Add '-217' to each side of the equation.
217 + -217 + x = 217.021197121 + -217

Combine like terms: 217 + -217 = 0
0 + x = 217.021197121 + -217
x = 217.021197121 + -217

Combine like terms: 217.021197121 + -217 = 0.021197121
x = 0.021197121

Simplifying
x = 0.021197121


Subproblem 2
x + 217 = -217.021197121

Simplifying
x + 217 = -217.021197121

Reorder the terms:
217 + x = -217.021197121

Solving
217 + x = -217.021197121

Solving for variable 'x'.

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

Add '-217' to each side of the equation.
217 + -217 + x = -217.021197121 + -217

Combine like terms: 217 + -217 = 0
0 + x = -217.021197121 + -217
x = -217.021197121 + -217

Combine like terms: -217.021197121 + -217 = -434.021197121
x = -434.021197121

Simplifying
x = -434.021197121


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.021197121, -434.021197121}
Solution
x = {0.021197121, -434.021197121}

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