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Simplifying 3x2 + -100x + 600 = 0 Reorder the terms: 600 + -100x + 3x2 = 0 Solving 600 + -100x + 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'. 200 + -33.33333333x + x2 = 0 Move the constant term to the right: Add '-200' to each side of the equation. 200 + -33.33333333x + -200 + x2 = 0 + -200 Reorder the terms: 200 + -200 + -33.33333333x + x2 = 0 + -200 Combine like terms: 200 + -200 = 0 0 + -33.33333333x + x2 = 0 + -200 -33.33333333x + x2 = 0 + -200 Combine like terms: 0 + -200 = -200 -33.33333333x + x2 = -200 The x term is -33.33333333x. Take half its coefficient (-16.66666667). Square it (277.7777779) and add it to both sides. Add '277.7777779' to each side of the equation. -33.33333333x + 277.7777779 + x2 = -200 + 277.7777779 Reorder the terms: 277.7777779 + -33.33333333x + x2 = -200 + 277.7777779 Combine like terms: -200 + 277.7777779 = 77.7777779 277.7777779 + -33.33333333x + x2 = 77.7777779 Factor a perfect square on the left side: (x + -16.66666667)(x + -16.66666667) = 77.7777779 Calculate the square root of the right side: 8.819171044 Break this problem into two subproblems by setting (x + -16.66666667) equal to 8.819171044 and -8.819171044.Subproblem 1
x + -16.66666667 = 8.819171044 Simplifying x + -16.66666667 = 8.819171044 Reorder the terms: -16.66666667 + x = 8.819171044 Solving -16.66666667 + x = 8.819171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = 8.819171044 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = 8.819171044 + 16.66666667 x = 8.819171044 + 16.66666667 Combine like terms: 8.819171044 + 16.66666667 = 25.485837714 x = 25.485837714 Simplifying x = 25.485837714Subproblem 2
x + -16.66666667 = -8.819171044 Simplifying x + -16.66666667 = -8.819171044 Reorder the terms: -16.66666667 + x = -8.819171044 Solving -16.66666667 + x = -8.819171044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.66666667' to each side of the equation. -16.66666667 + 16.66666667 + x = -8.819171044 + 16.66666667 Combine like terms: -16.66666667 + 16.66666667 = 0.00000000 0.00000000 + x = -8.819171044 + 16.66666667 x = -8.819171044 + 16.66666667 Combine like terms: -8.819171044 + 16.66666667 = 7.847495626 x = 7.847495626 Simplifying x = 7.847495626Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.485837714, 7.847495626}
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