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Simplifying 3x2 + -50x = 150 Reorder the terms: -50x + 3x2 = 150 Solving -50x + 3x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + -50x + 3x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + -50x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -50 + -16.66666667x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -16.66666667x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -16.66666667x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -16.66666667x + x2 = 0 + 50 -16.66666667x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -16.66666667x + x2 = 50 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 = 50 + 69.44444447 Reorder the terms: 69.44444447 + -16.66666667x + x2 = 50 + 69.44444447 Combine like terms: 50 + 69.44444447 = 119.44444447 69.44444447 + -16.66666667x + x2 = 119.44444447 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 119.44444447 Calculate the square root of the right side: 10.929064208 Break this problem into two subproblems by setting (x + -8.333333335) equal to 10.929064208 and -10.929064208.Subproblem 1
x + -8.333333335 = 10.929064208 Simplifying x + -8.333333335 = 10.929064208 Reorder the terms: -8.333333335 + x = 10.929064208 Solving -8.333333335 + x = 10.929064208 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 = 10.929064208 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 10.929064208 + 8.333333335 x = 10.929064208 + 8.333333335 Combine like terms: 10.929064208 + 8.333333335 = 19.262397543 x = 19.262397543 Simplifying x = 19.262397543Subproblem 2
x + -8.333333335 = -10.929064208 Simplifying x + -8.333333335 = -10.929064208 Reorder the terms: -8.333333335 + x = -10.929064208 Solving -8.333333335 + x = -10.929064208 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 = -10.929064208 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -10.929064208 + 8.333333335 x = -10.929064208 + 8.333333335 Combine like terms: -10.929064208 + 8.333333335 = -2.595730873 x = -2.595730873 Simplifying x = -2.595730873Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.262397543, -2.595730873}
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