49x^2-119x-80=0

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Solution for 49x^2-119x-80=0 equation:


Simplifying
49x2 + -119x + -80 = 0

Reorder the terms:
-80 + -119x + 49x2 = 0

Solving
-80 + -119x + 49x2 = 0

Solving for variable 'x'.

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

Divide each side by '49'.
-1.632653061 + -2.428571429x + x2 = 0

Move the constant term to the right:

Add '1.632653061' to each side of the equation.
-1.632653061 + -2.428571429x + 1.632653061 + x2 = 0 + 1.632653061

Reorder the terms:
-1.632653061 + 1.632653061 + -2.428571429x + x2 = 0 + 1.632653061

Combine like terms: -1.632653061 + 1.632653061 = 0.000000000
0.000000000 + -2.428571429x + x2 = 0 + 1.632653061
-2.428571429x + x2 = 0 + 1.632653061

Combine like terms: 0 + 1.632653061 = 1.632653061
-2.428571429x + x2 = 1.632653061

The x term is -2.428571429x.  Take half its coefficient (-1.214285715).
Square it (1.474489798) and add it to both sides.

Add '1.474489798' to each side of the equation.
-2.428571429x + 1.474489798 + x2 = 1.632653061 + 1.474489798

Reorder the terms:
1.474489798 + -2.428571429x + x2 = 1.632653061 + 1.474489798

Combine like terms: 1.632653061 + 1.474489798 = 3.107142859
1.474489798 + -2.428571429x + x2 = 3.107142859

Factor a perfect square on the left side:
(x + -1.214285715)(x + -1.214285715) = 3.107142859

Calculate the square root of the right side: 1.762708955

Break this problem into two subproblems by setting 
(x + -1.214285715) equal to 1.762708955 and -1.762708955.

Subproblem 1

x + -1.214285715 = 1.762708955 Simplifying x + -1.214285715 = 1.762708955 Reorder the terms: -1.214285715 + x = 1.762708955 Solving -1.214285715 + x = 1.762708955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = 1.762708955 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = 1.762708955 + 1.214285715 x = 1.762708955 + 1.214285715 Combine like terms: 1.762708955 + 1.214285715 = 2.97699467 x = 2.97699467 Simplifying x = 2.97699467

Subproblem 2

x + -1.214285715 = -1.762708955 Simplifying x + -1.214285715 = -1.762708955 Reorder the terms: -1.214285715 + x = -1.762708955 Solving -1.214285715 + x = -1.762708955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.214285715' to each side of the equation. -1.214285715 + 1.214285715 + x = -1.762708955 + 1.214285715 Combine like terms: -1.214285715 + 1.214285715 = 0.000000000 0.000000000 + x = -1.762708955 + 1.214285715 x = -1.762708955 + 1.214285715 Combine like terms: -1.762708955 + 1.214285715 = -0.54842324 x = -0.54842324 Simplifying x = -0.54842324

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.97699467, -0.54842324}

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