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Simplifying 3x2 + 44x + -6378 = 0 Reorder the terms: -6378 + 44x + 3x2 = 0 Solving -6378 + 44x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2126 + 14.66666667x + x2 = 0 Move the constant term to the right: Add '2126' to each side of the equation. -2126 + 14.66666667x + 2126 + x2 = 0 + 2126 Reorder the terms: -2126 + 2126 + 14.66666667x + x2 = 0 + 2126 Combine like terms: -2126 + 2126 = 0 0 + 14.66666667x + x2 = 0 + 2126 14.66666667x + x2 = 0 + 2126 Combine like terms: 0 + 2126 = 2126 14.66666667x + x2 = 2126 The x term is 14.66666667x. Take half its coefficient (7.333333335). Square it (53.77777780) and add it to both sides. Add '53.77777780' to each side of the equation. 14.66666667x + 53.77777780 + x2 = 2126 + 53.77777780 Reorder the terms: 53.77777780 + 14.66666667x + x2 = 2126 + 53.77777780 Combine like terms: 2126 + 53.77777780 = 2179.7777778 53.77777780 + 14.66666667x + x2 = 2179.7777778 Factor a perfect square on the left side: (x + 7.333333335)(x + 7.333333335) = 2179.7777778 Calculate the square root of the right side: 46.688090321 Break this problem into two subproblems by setting (x + 7.333333335) equal to 46.688090321 and -46.688090321.Subproblem 1
x + 7.333333335 = 46.688090321 Simplifying x + 7.333333335 = 46.688090321 Reorder the terms: 7.333333335 + x = 46.688090321 Solving 7.333333335 + x = 46.688090321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = 46.688090321 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = 46.688090321 + -7.333333335 x = 46.688090321 + -7.333333335 Combine like terms: 46.688090321 + -7.333333335 = 39.354756986 x = 39.354756986 Simplifying x = 39.354756986Subproblem 2
x + 7.333333335 = -46.688090321 Simplifying x + 7.333333335 = -46.688090321 Reorder the terms: 7.333333335 + x = -46.688090321 Solving 7.333333335 + x = -46.688090321 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.333333335' to each side of the equation. 7.333333335 + -7.333333335 + x = -46.688090321 + -7.333333335 Combine like terms: 7.333333335 + -7.333333335 = 0.000000000 0.000000000 + x = -46.688090321 + -7.333333335 x = -46.688090321 + -7.333333335 Combine like terms: -46.688090321 + -7.333333335 = -54.021423656 x = -54.021423656 Simplifying x = -54.021423656Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.354756986, -54.021423656}
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