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