10x^2-139x-390=0

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Solution for 10x^2-139x-390=0 equation: 


Simplifying
10x2 + -139x + -390 = 0

Reorder the terms:
-390 + -139x + 10x2 = 0

Solving
-390 + -139x + 10x2 = 0

Solving for variable 'x'.

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

Divide each side by '10'.
-39 + -13.9x + x2 = 0

Move the constant term to the right:

Add '39' to each side of the equation.
-39 + -13.9x + 39 + x2 = 0 + 39

Reorder the terms:
-39 + 39 + -13.9x + x2 = 0 + 39

Combine like terms: -39 + 39 = 0
0 + -13.9x + x2 = 0 + 39
-13.9x + x2 = 0 + 39

Combine like terms: 0 + 39 = 39
-13.9x + x2 = 39

The x term is -13.9x.  Take half its coefficient (-6.95).
Square it (48.3025) and add it to both sides.

Add '48.3025' to each side of the equation.
-13.9x + 48.3025 + x2 = 39 + 48.3025

Reorder the terms:
48.3025 + -13.9x + x2 = 39 + 48.3025

Combine like terms: 39 + 48.3025 = 87.3025
48.3025 + -13.9x + x2 = 87.3025

Factor a perfect square on the left side:
(x + -6.95)(x + -6.95) = 87.3025

Calculate the square root of the right side: 9.343580684

Break this problem into two subproblems by setting 
(x + -6.95) equal to 9.343580684 and -9.343580684.


Subproblem 1
x + -6.95 = 9.343580684

Simplifying
x + -6.95 = 9.343580684

Reorder the terms:
-6.95 + x = 9.343580684

Solving
-6.95 + x = 9.343580684

Solving for variable 'x'.

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

Add '6.95' to each side of the equation.
-6.95 + 6.95 + x = 9.343580684 + 6.95

Combine like terms: -6.95 + 6.95 = 0.00
0.00 + x = 9.343580684 + 6.95
x = 9.343580684 + 6.95

Combine like terms: 9.343580684 + 6.95 = 16.293580684
x = 16.293580684

Simplifying
x = 16.293580684


Subproblem 2
x + -6.95 = -9.343580684

Simplifying
x + -6.95 = -9.343580684

Reorder the terms:
-6.95 + x = -9.343580684

Solving
-6.95 + x = -9.343580684

Solving for variable 'x'.

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

Add '6.95' to each side of the equation.
-6.95 + 6.95 + x = -9.343580684 + 6.95

Combine like terms: -6.95 + 6.95 = 0.00
0.00 + x = -9.343580684 + 6.95
x = -9.343580684 + 6.95

Combine like terms: -9.343580684 + 6.95 = -2.393580684
x = -2.393580684

Simplifying
x = -2.393580684


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.293580684, -2.393580684}

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