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Simplifying 3x2 + -200x + 2400 = 0 Reorder the terms: 2400 + -200x + 3x2 = 0 Solving 2400 + -200x + 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'. 800 + -66.66666667x + x2 = 0 Move the constant term to the right: Add '-800' to each side of the equation. 800 + -66.66666667x + -800 + x2 = 0 + -800 Reorder the terms: 800 + -800 + -66.66666667x + x2 = 0 + -800 Combine like terms: 800 + -800 = 0 0 + -66.66666667x + x2 = 0 + -800 -66.66666667x + x2 = 0 + -800 Combine like terms: 0 + -800 = -800 -66.66666667x + x2 = -800 The x term is -66.66666667x. Take half its coefficient (-33.33333334). Square it (1111.111112) and add it to both sides. Add '1111.111112' to each side of the equation. -66.66666667x + 1111.111112 + x2 = -800 + 1111.111112 Reorder the terms: 1111.111112 + -66.66666667x + x2 = -800 + 1111.111112 Combine like terms: -800 + 1111.111112 = 311.111112 1111.111112 + -66.66666667x + x2 = 311.111112 Factor a perfect square on the left side: (x + -33.33333334)(x + -33.33333334) = 311.111112 Calculate the square root of the right side: 17.638342099 Break this problem into two subproblems by setting (x + -33.33333334) equal to 17.638342099 and -17.638342099.Subproblem 1
x + -33.33333334 = 17.638342099 Simplifying x + -33.33333334 = 17.638342099 Reorder the terms: -33.33333334 + x = 17.638342099 Solving -33.33333334 + x = 17.638342099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = 17.638342099 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = 17.638342099 + 33.33333334 x = 17.638342099 + 33.33333334 Combine like terms: 17.638342099 + 33.33333334 = 50.971675439 x = 50.971675439 Simplifying x = 50.971675439Subproblem 2
x + -33.33333334 = -17.638342099 Simplifying x + -33.33333334 = -17.638342099 Reorder the terms: -33.33333334 + x = -17.638342099 Solving -33.33333334 + x = -17.638342099 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33.33333334' to each side of the equation. -33.33333334 + 33.33333334 + x = -17.638342099 + 33.33333334 Combine like terms: -33.33333334 + 33.33333334 = 0.00000000 0.00000000 + x = -17.638342099 + 33.33333334 x = -17.638342099 + 33.33333334 Combine like terms: -17.638342099 + 33.33333334 = 15.694991241 x = 15.694991241 Simplifying x = 15.694991241Solution
The solution to the problem is based on the solutions from the subproblems. x = {50.971675439, 15.694991241}
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