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Simplifying 3x2 + -50x = 168 Reorder the terms: -50x + 3x2 = 168 Solving -50x + 3x2 = 168 Solving for variable 'x'. Reorder the terms: -168 + -50x + 3x2 = 168 + -168 Combine like terms: 168 + -168 = 0 -168 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -56 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + -16.66666667x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -16.66666667x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -16.66666667x + x2 = 0 + 56 -16.66666667x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -16.66666667x + x2 = 56 The x term is -16.66666667x. Take half its coefficient (-8.333333335). Square it (69.44444447) and add it to both sides. Add '69.44444447' to each side of the equation. -16.66666667x + 69.44444447 + x2 = 56 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 56 + 69.44444447 Combine like terms: 56 + 69.44444447 = 125.44444447 69.44444447 + -16.66666667x + x2 = 125.44444447 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 125.44444447 Calculate the square root of the right side: 11.200198412 Break this problem into two subproblems by setting (x + -8.333333335) equal to 11.200198412 and -11.200198412.Subproblem 1
x + -8.333333335 = 11.200198412 Simplifying x + -8.333333335 = 11.200198412 Reorder the terms: -8.333333335 + x = 11.200198412 Solving -8.333333335 + x = 11.200198412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = 11.200198412 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 11.200198412 + 8.333333335 x = 11.200198412 + 8.333333335 Combine like terms: 11.200198412 + 8.333333335 = 19.533531747 x = 19.533531747 Simplifying x = 19.533531747Subproblem 2
x + -8.333333335 = -11.200198412 Simplifying x + -8.333333335 = -11.200198412 Reorder the terms: -8.333333335 + x = -11.200198412 Solving -8.333333335 + x = -11.200198412 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.333333335' to each side of the equation. -8.333333335 + 8.333333335 + x = -11.200198412 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -11.200198412 + 8.333333335 x = -11.200198412 + 8.333333335 Combine like terms: -11.200198412 + 8.333333335 = -2.866865077 x = -2.866865077 Simplifying x = -2.866865077Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.533531747, -2.866865077}
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