22x^2+60500x-3410=0

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Solution for 22x^2+60500x-3410=0 equation: 


Simplifying
22x2 + 60500x + -3410 = 0

Reorder the terms:
-3410 + 60500x + 22x2 = 0

Solving
-3410 + 60500x + 22x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '22'.
22(-155 + 2750x + x2) = 0

Ignore the factor 22.

Subproblem 1
Set the factor '(-155 + 2750x + x2)' equal to zero and attempt to solve:

Simplifying
-155 + 2750x + x2 = 0

Solving
-155 + 2750x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '155' to each side of the equation.
-155 + 2750x + 155 + x2 = 0 + 155

Reorder the terms:
-155 + 155 + 2750x + x2 = 0 + 155

Combine like terms: -155 + 155 = 0
0 + 2750x + x2 = 0 + 155
2750x + x2 = 0 + 155

Combine like terms: 0 + 155 = 155
2750x + x2 = 155

The x term is 2750x.  Take half its coefficient (1375).
Square it (1890625) and add it to both sides.

Add '1890625' to each side of the equation.
2750x + 1890625 + x2 = 155 + 1890625

Reorder the terms:
1890625 + 2750x + x2 = 155 + 1890625

Combine like terms: 155 + 1890625 = 1890780
1890625 + 2750x + x2 = 1890780

Factor a perfect square on the left side:
(x + 1375)(x + 1375) = 1890780

Calculate the square root of the right side: 1375.056362481

Break this problem into two subproblems by setting 
(x + 1375) equal to 1375.056362481 and -1375.056362481.


Subproblem 1
x + 1375 = 1375.056362481

Simplifying
x + 1375 = 1375.056362481

Reorder the terms:
1375 + x = 1375.056362481

Solving
1375 + x = 1375.056362481

Solving for variable 'x'.

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

Add '-1375' to each side of the equation.
1375 + -1375 + x = 1375.056362481 + -1375

Combine like terms: 1375 + -1375 = 0
0 + x = 1375.056362481 + -1375
x = 1375.056362481 + -1375

Combine like terms: 1375.056362481 + -1375 = 0.056362481
x = 0.056362481

Simplifying
x = 0.056362481


Subproblem 2
x + 1375 = -1375.056362481

Simplifying
x + 1375 = -1375.056362481

Reorder the terms:
1375 + x = -1375.056362481

Solving
1375 + x = -1375.056362481

Solving for variable 'x'.

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

Add '-1375' to each side of the equation.
1375 + -1375 + x = -1375.056362481 + -1375

Combine like terms: 1375 + -1375 = 0
0 + x = -1375.056362481 + -1375
x = -1375.056362481 + -1375

Combine like terms: -1375.056362481 + -1375 = -2750.056362481
x = -2750.056362481

Simplifying
x = -2750.056362481


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.056362481, -2750.056362481}
Solution
x = {0.056362481, -2750.056362481}

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