39x^2-460x-2380=0

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Solution for 39x^2-460x-2380=0 equation:


Simplifying
39x2 + -460x + -2380 = 0

Reorder the terms:
-2380 + -460x + 39x2 = 0

Solving
-2380 + -460x + 39x2 = 0

Solving for variable 'x'.

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

Divide each side by '39'.
-61.02564103 + -11.79487179x + x2 = 0

Move the constant term to the right:

Add '61.02564103' to each side of the equation.
-61.02564103 + -11.79487179x + 61.02564103 + x2 = 0 + 61.02564103

Reorder the terms:
-61.02564103 + 61.02564103 + -11.79487179x + x2 = 0 + 61.02564103

Combine like terms: -61.02564103 + 61.02564103 = 0.00000000
0.00000000 + -11.79487179x + x2 = 0 + 61.02564103
-11.79487179x + x2 = 0 + 61.02564103

Combine like terms: 0 + 61.02564103 = 61.02564103
-11.79487179x + x2 = 61.02564103

The x term is -11.79487179x.  Take half its coefficient (-5.897435895).
Square it (34.77975014) and add it to both sides.

Add '34.77975014' to each side of the equation.
-11.79487179x + 34.77975014 + x2 = 61.02564103 + 34.77975014

Reorder the terms:
34.77975014 + -11.79487179x + x2 = 61.02564103 + 34.77975014

Combine like terms: 61.02564103 + 34.77975014 = 95.80539117
34.77975014 + -11.79487179x + x2 = 95.80539117

Factor a perfect square on the left side:
(x + -5.897435895)(x + -5.897435895) = 95.80539117

Calculate the square root of the right side: 9.788022843

Break this problem into two subproblems by setting 
(x + -5.897435895) equal to 9.788022843 and -9.788022843.

Subproblem 1

x + -5.897435895 = 9.788022843 Simplifying x + -5.897435895 = 9.788022843 Reorder the terms: -5.897435895 + x = 9.788022843 Solving -5.897435895 + x = 9.788022843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.897435895' to each side of the equation. -5.897435895 + 5.897435895 + x = 9.788022843 + 5.897435895 Combine like terms: -5.897435895 + 5.897435895 = 0.000000000 0.000000000 + x = 9.788022843 + 5.897435895 x = 9.788022843 + 5.897435895 Combine like terms: 9.788022843 + 5.897435895 = 15.685458738 x = 15.685458738 Simplifying x = 15.685458738

Subproblem 2

x + -5.897435895 = -9.788022843 Simplifying x + -5.897435895 = -9.788022843 Reorder the terms: -5.897435895 + x = -9.788022843 Solving -5.897435895 + x = -9.788022843 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.897435895' to each side of the equation. -5.897435895 + 5.897435895 + x = -9.788022843 + 5.897435895 Combine like terms: -5.897435895 + 5.897435895 = 0.000000000 0.000000000 + x = -9.788022843 + 5.897435895 x = -9.788022843 + 5.897435895 Combine like terms: -9.788022843 + 5.897435895 = -3.890586948 x = -3.890586948 Simplifying x = -3.890586948

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.685458738, -3.890586948}

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