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Simplifying 150 + -50x + 3x2 = 0 Solving 150 + -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'. 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 = 19.44444447 69.44444447 + -16.66666667x + x2 = 19.44444447 Factor a perfect square on the left side: (x + -8.333333335)(x + -8.333333335) = 19.44444447 Calculate the square root of the right side: 4.409585521 Break this problem into two subproblems by setting (x + -8.333333335) equal to 4.409585521 and -4.409585521.Subproblem 1
x + -8.333333335 = 4.409585521 Simplifying x + -8.333333335 = 4.409585521 Reorder the terms: -8.333333335 + x = 4.409585521 Solving -8.333333335 + x = 4.409585521 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 = 4.409585521 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = 4.409585521 + 8.333333335 x = 4.409585521 + 8.333333335 Combine like terms: 4.409585521 + 8.333333335 = 12.742918856 x = 12.742918856 Simplifying x = 12.742918856Subproblem 2
x + -8.333333335 = -4.409585521 Simplifying x + -8.333333335 = -4.409585521 Reorder the terms: -8.333333335 + x = -4.409585521 Solving -8.333333335 + x = -4.409585521 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 = -4.409585521 + 8.333333335 Combine like terms: -8.333333335 + 8.333333335 = 0.000000000 0.000000000 + x = -4.409585521 + 8.333333335 x = -4.409585521 + 8.333333335 Combine like terms: -4.409585521 + 8.333333335 = 3.923747814 x = 3.923747814 Simplifying x = 3.923747814Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.742918856, 3.923747814}
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