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Simplifying 0 = 3x2 + -50x + -154 Reorder the terms: 0 = -154 + -50x + 3x2 Solving 0 = -154 + -50x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 154 = 154 154 + 50x + -3x2 = -154 + -50x + 3x2 + 154 + 50x + -3x2 Reorder the terms: 154 + 50x + -3x2 = -154 + 154 + -50x + 50x + 3x2 + -3x2 Combine like terms: -154 + 154 = 0 154 + 50x + -3x2 = 0 + -50x + 50x + 3x2 + -3x2 154 + 50x + -3x2 = -50x + 50x + 3x2 + -3x2 Combine like terms: -50x + 50x = 0 154 + 50x + -3x2 = 0 + 3x2 + -3x2 154 + 50x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 154 + 50x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -51.33333333 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '51.33333333' to each side of the equation. -51.33333333 + -16.66666667x + 51.33333333 + x2 = 0 + 51.33333333 Reorder the terms: -51.33333333 + 51.33333333 + -16.66666667x + x2 = 0 + 51.33333333 Combine like terms: -51.33333333 + 51.33333333 = 0.00000000 0.00000000 + -16.66666667x + x2 = 0 + 51.33333333 -16.66666667x + x2 = 0 + 51.33333333 Combine like terms: 0 + 51.33333333 = 51.33333333 -16.66666667x + x2 = 51.33333333 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 = 51.33333333 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 51.33333333 + 69.44444447 Combine like terms: 51.33333333 + 69.44444447 = 120.7777778 69.44444447 + -16.66666667x + x2 = 120.7777778 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 120.7777778 Calculate the square root of the right side: 10.989894349 Break this problem into two subproblems by setting (x + -8.333333335) equal to 10.989894349 and -10.989894349.Subproblem 1
x + -8.333333335 = 10.989894349 Simplifying x + -8.333333335 = 10.989894349 Reorder the terms: -8.333333335 + x = 10.989894349 Solving -8.333333335 + x = 10.989894349 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 = 10.989894349 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 10.989894349 + 8.333333335 x = 10.989894349 + 8.333333335 Combine like terms: 10.989894349 + 8.333333335 = 19.323227684 x = 19.323227684 Simplifying x = 19.323227684Subproblem 2
x + -8.333333335 = -10.989894349 Simplifying x + -8.333333335 = -10.989894349 Reorder the terms: -8.333333335 + x = -10.989894349 Solving -8.333333335 + x = -10.989894349 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 = -10.989894349 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -10.989894349 + 8.333333335 x = -10.989894349 + 8.333333335 Combine like terms: -10.989894349 + 8.333333335 = -2.656561014 x = -2.656561014 Simplifying x = -2.656561014Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.323227684, -2.656561014}
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