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Simplifying 3x2 + -50x + -105 = 0 Reorder the terms: -105 + -50x + 3x2 = 0 Solving -105 + -50x + 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'. -35 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '35' to each side of the equation. -35 + -16.66666667x + 35 + x2 = 0 + 35 Reorder the terms: -35 + 35 + -16.66666667x + x2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -16.66666667x + x2 = 0 + 35 -16.66666667x + x2 = 0 + 35 Combine like terms: 0 + 35 = 35 -16.66666667x + x2 = 35 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 = 35 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 35 + 69.44444447 Combine like terms: 35 + 69.44444447 = 104.44444447 69.44444447 + -16.66666667x + x2 = 104.44444447 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 104.44444447 Calculate the square root of the right side: 10.219806479 Break this problem into two subproblems by setting (x + -8.333333335) equal to 10.219806479 and -10.219806479.Subproblem 1
x + -8.333333335 = 10.219806479 Simplifying x + -8.333333335 = 10.219806479 Reorder the terms: -8.333333335 + x = 10.219806479 Solving -8.333333335 + x = 10.219806479 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 = 10.219806479 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 10.219806479 + 8.333333335 x = 10.219806479 + 8.333333335 Combine like terms: 10.219806479 + 8.333333335 = 18.553139814 x = 18.553139814 Simplifying x = 18.553139814Subproblem 2
x + -8.333333335 = -10.219806479 Simplifying x + -8.333333335 = -10.219806479 Reorder the terms: -8.333333335 + x = -10.219806479 Solving -8.333333335 + x = -10.219806479 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 = -10.219806479 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -10.219806479 + 8.333333335 x = -10.219806479 + 8.333333335 Combine like terms: -10.219806479 + 8.333333335 = -1.886473144 x = -1.886473144 Simplifying x = -1.886473144Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.553139814, -1.886473144}
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