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Simplifying 3x2 + -260x + 1200 = 0 Reorder the terms: 1200 + -260x + 3x2 = 0 Solving 1200 + -260x + 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'. 400 + -86.66666667x + x2 = 0 Move the constant term to the right: Add '-400' to each side of the equation. 400 + -86.66666667x + -400 + x2 = 0 + -400 Reorder the terms: 400 + -400 + -86.66666667x + x2 = 0 + -400 Combine like terms: 400 + -400 = 0 0 + -86.66666667x + x2 = 0 + -400 -86.66666667x + x2 = 0 + -400 Combine like terms: 0 + -400 = -400 -86.66666667x + x2 = -400 The x term is -86.66666667x. Take half its coefficient (-43.33333334). Square it (1877.777778) and add it to both sides. Add '1877.777778' to each side of the equation. -86.66666667x + 1877.777778 + x2 = -400 + 1877.777778 Reorder the terms: 1877.777778 + -86.66666667x + x2 = -400 + 1877.777778 Combine like terms: -400 + 1877.777778 = 1477.777778 1877.777778 + -86.66666667x + x2 = 1477.777778 Factor a perfect square on the left side: (x + -43.33333334)(x + -43.33333334) = 1477.777778 Calculate the square root of the right side: 38.441875318 Break this problem into two subproblems by setting (x + -43.33333334) equal to 38.441875318 and -38.441875318.Subproblem 1
x + -43.33333334 = 38.441875318 Simplifying x + -43.33333334 = 38.441875318 Reorder the terms: -43.33333334 + x = 38.441875318 Solving -43.33333334 + x = 38.441875318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.33333334' to each side of the equation. -43.33333334 + 43.33333334 + x = 38.441875318 + 43.33333334 Combine like terms: -43.33333334 + 43.33333334 = 0.00000000 0.00000000 + x = 38.441875318 + 43.33333334 x = 38.441875318 + 43.33333334 Combine like terms: 38.441875318 + 43.33333334 = 81.775208658 x = 81.775208658 Simplifying x = 81.775208658Subproblem 2
x + -43.33333334 = -38.441875318 Simplifying x + -43.33333334 = -38.441875318 Reorder the terms: -43.33333334 + x = -38.441875318 Solving -43.33333334 + x = -38.441875318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43.33333334' to each side of the equation. -43.33333334 + 43.33333334 + x = -38.441875318 + 43.33333334 Combine like terms: -43.33333334 + 43.33333334 = 0.00000000 0.00000000 + x = -38.441875318 + 43.33333334 x = -38.441875318 + 43.33333334 Combine like terms: -38.441875318 + 43.33333334 = 4.891458022 x = 4.891458022 Simplifying x = 4.891458022Solution
The solution to the problem is based on the solutions from the subproblems. x = {81.775208658, 4.891458022}
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