3x^2-41x=-100

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Solution for 3x^2-41x=-100 equation:


Simplifying
3x2 + -41x = -100

Reorder the terms:
-41x + 3x2 = -100

Solving
-41x + 3x2 = -100

Solving for variable 'x'.

Reorder the terms:
100 + -41x + 3x2 = -100 + 100

Combine like terms: -100 + 100 = 0
100 + -41x + 3x2 = 0

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

Divide each side by '3'.
33.33333333 + -13.66666667x + x2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -13.66666667x + -33.33333333 + x2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -13.66666667x + x2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -13.66666667x + x2 = 0 + -33.33333333
-13.66666667x + x2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-13.66666667x + x2 = -33.33333333

The x term is -13.66666667x.  Take half its coefficient (-6.833333335).
Square it (46.69444447) and add it to both sides.

Add '46.69444447' to each side of the equation.
-13.66666667x + 46.69444447 + x2 = -33.33333333 + 46.69444447

Reorder the terms:
46.69444447 + -13.66666667x + x2 = -33.33333333 + 46.69444447

Combine like terms: -33.33333333 + 46.69444447 = 13.36111114
46.69444447 + -13.66666667x + x2 = 13.36111114

Factor a perfect square on the left side:
(x + -6.833333335)(x + -6.833333335) = 13.36111114

Calculate the square root of the right side: 3.655285371

Break this problem into two subproblems by setting 
(x + -6.833333335) equal to 3.655285371 and -3.655285371.

Subproblem 1

x + -6.833333335 = 3.655285371 Simplifying x + -6.833333335 = 3.655285371 Reorder the terms: -6.833333335 + x = 3.655285371 Solving -6.833333335 + x = 3.655285371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = 3.655285371 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 3.655285371 + 6.833333335 x = 3.655285371 + 6.833333335 Combine like terms: 3.655285371 + 6.833333335 = 10.488618706 x = 10.488618706 Simplifying x = 10.488618706

Subproblem 2

x + -6.833333335 = -3.655285371 Simplifying x + -6.833333335 = -3.655285371 Reorder the terms: -6.833333335 + x = -3.655285371 Solving -6.833333335 + x = -3.655285371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.833333335' to each side of the equation. -6.833333335 + 6.833333335 + x = -3.655285371 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -3.655285371 + 6.833333335 x = -3.655285371 + 6.833333335 Combine like terms: -3.655285371 + 6.833333335 = 3.178047964 x = 3.178047964 Simplifying x = 3.178047964

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.488618706, 3.178047964}

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