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Simplifying 3x2 + -41x = 110 Reorder the terms: -41x + 3x2 = 110 Solving -41x + 3x2 = 110 Solving for variable 'x'. Reorder the terms: -110 + -41x + 3x2 = 110 + -110 Combine like terms: 110 + -110 = 0 -110 + -41x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -36.66666667 + -13.66666667x + x2 = 0 Move the constant term to the right: Add '36.66666667' to each side of the equation. -36.66666667 + -13.66666667x + 36.66666667 + x2 = 0 + 36.66666667 Reorder the terms: -36.66666667 + 36.66666667 + -13.66666667x + x2 = 0 + 36.66666667 Combine like terms: -36.66666667 + 36.66666667 = 0.00000000 0.00000000 + -13.66666667x + x2 = 0 + 36.66666667 -13.66666667x + x2 = 0 + 36.66666667 Combine like terms: 0 + 36.66666667 = 36.66666667 -13.66666667x + x2 = 36.66666667 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 = 36.66666667 + 46.69444447 Reorder the terms: 46.69444447 + -13.66666667x + x2 = 36.66666667 + 46.69444447 Combine like terms: 36.66666667 + 46.69444447 = 83.36111114 46.69444447 + -13.66666667x + x2 = 83.36111114 Factor a perfect square on the left side: (x + -6.833333335)(x + -6.833333335) = 83.36111114 Calculate the square root of the right side: 9.130230618 Break this problem into two subproblems by setting (x + -6.833333335) equal to 9.130230618 and -9.130230618.Subproblem 1
x + -6.833333335 = 9.130230618 Simplifying x + -6.833333335 = 9.130230618 Reorder the terms: -6.833333335 + x = 9.130230618 Solving -6.833333335 + x = 9.130230618 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 = 9.130230618 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = 9.130230618 + 6.833333335 x = 9.130230618 + 6.833333335 Combine like terms: 9.130230618 + 6.833333335 = 15.963563953 x = 15.963563953 Simplifying x = 15.963563953Subproblem 2
x + -6.833333335 = -9.130230618 Simplifying x + -6.833333335 = -9.130230618 Reorder the terms: -6.833333335 + x = -9.130230618 Solving -6.833333335 + x = -9.130230618 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 = -9.130230618 + 6.833333335 Combine like terms: -6.833333335 + 6.833333335 = 0.000000000 0.000000000 + x = -9.130230618 + 6.833333335 x = -9.130230618 + 6.833333335 Combine like terms: -9.130230618 + 6.833333335 = -2.296897283 x = -2.296897283 Simplifying x = -2.296897283Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.963563953, -2.296897283}
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