5x^2-605x-949=0

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Solution for 5x^2-605x-949=0 equation:


Simplifying
5x2 + -605x + -949 = 0

Reorder the terms:
-949 + -605x + 5x2 = 0

Solving
-949 + -605x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-189.8 + -121x + x2 = 0

Move the constant term to the right:

Add '189.8' to each side of the equation.
-189.8 + -121x + 189.8 + x2 = 0 + 189.8

Reorder the terms:
-189.8 + 189.8 + -121x + x2 = 0 + 189.8

Combine like terms: -189.8 + 189.8 = 0.0
0.0 + -121x + x2 = 0 + 189.8
-121x + x2 = 0 + 189.8

Combine like terms: 0 + 189.8 = 189.8
-121x + x2 = 189.8

The x term is -121x.  Take half its coefficient (-60.5).
Square it (3660.25) and add it to both sides.

Add '3660.25' to each side of the equation.
-121x + 3660.25 + x2 = 189.8 + 3660.25

Reorder the terms:
3660.25 + -121x + x2 = 189.8 + 3660.25

Combine like terms: 189.8 + 3660.25 = 3850.05
3660.25 + -121x + x2 = 3850.05

Factor a perfect square on the left side:
(x + -60.5)(x + -60.5) = 3850.05

Calculate the square root of the right side: 62.04877114

Break this problem into two subproblems by setting 
(x + -60.5) equal to 62.04877114 and -62.04877114.

Subproblem 1

x + -60.5 = 62.04877114 Simplifying x + -60.5 = 62.04877114 Reorder the terms: -60.5 + x = 62.04877114 Solving -60.5 + x = 62.04877114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.5' to each side of the equation. -60.5 + 60.5 + x = 62.04877114 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = 62.04877114 + 60.5 x = 62.04877114 + 60.5 Combine like terms: 62.04877114 + 60.5 = 122.54877114 x = 122.54877114 Simplifying x = 122.54877114

Subproblem 2

x + -60.5 = -62.04877114 Simplifying x + -60.5 = -62.04877114 Reorder the terms: -60.5 + x = -62.04877114 Solving -60.5 + x = -62.04877114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '60.5' to each side of the equation. -60.5 + 60.5 + x = -62.04877114 + 60.5 Combine like terms: -60.5 + 60.5 = 0.0 0.0 + x = -62.04877114 + 60.5 x = -62.04877114 + 60.5 Combine like terms: -62.04877114 + 60.5 = -1.54877114 x = -1.54877114 Simplifying x = -1.54877114

Solution

The solution to the problem is based on the solutions from the subproblems. x = {122.54877114, -1.54877114}

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