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Simplifying 4.905x2 + -53x + 126 = 0 Reorder the terms: 126 + -53x + 4.905x2 = 0 Solving 126 + -53x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. 25.68807339 + -10.80530071x + x2 = 0 Move the constant term to the right: Add '-25.68807339' to each side of the equation. 25.68807339 + -10.80530071x + -25.68807339 + x2 = 0 + -25.68807339 Reorder the terms: 25.68807339 + -25.68807339 + -10.80530071x + x2 = 0 + -25.68807339 Combine like terms: 25.68807339 + -25.68807339 = 0.00000000 0.00000000 + -10.80530071x + x2 = 0 + -25.68807339 -10.80530071x + x2 = 0 + -25.68807339 Combine like terms: 0 + -25.68807339 = -25.68807339 -10.80530071x + x2 = -25.68807339 The x term is -10.80530071x. Take half its coefficient (-5.402650355). Square it (29.18863086) and add it to both sides. Add '29.18863086' to each side of the equation. -10.80530071x + 29.18863086 + x2 = -25.68807339 + 29.18863086 Reorder the terms: 29.18863086 + -10.80530071x + x2 = -25.68807339 + 29.18863086 Combine like terms: -25.68807339 + 29.18863086 = 3.50055747 29.18863086 + -10.80530071x + x2 = 3.50055747 Factor a perfect square on the left side: (x + -5.402650355)(x + -5.402650355) = 3.50055747 Calculate the square root of the right side: 1.870977678 Break this problem into two subproblems by setting (x + -5.402650355) equal to 1.870977678 and -1.870977678.Subproblem 1
x + -5.402650355 = 1.870977678 Simplifying x + -5.402650355 = 1.870977678 Reorder the terms: -5.402650355 + x = 1.870977678 Solving -5.402650355 + x = 1.870977678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.402650355' to each side of the equation. -5.402650355 + 5.402650355 + x = 1.870977678 + 5.402650355 Combine like terms: -5.402650355 + 5.402650355 = 0.000000000 0.000000000 + x = 1.870977678 + 5.402650355 x = 1.870977678 + 5.402650355 Combine like terms: 1.870977678 + 5.402650355 = 7.273628033 x = 7.273628033 Simplifying x = 7.273628033Subproblem 2
x + -5.402650355 = -1.870977678 Simplifying x + -5.402650355 = -1.870977678 Reorder the terms: -5.402650355 + x = -1.870977678 Solving -5.402650355 + x = -1.870977678 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.402650355' to each side of the equation. -5.402650355 + 5.402650355 + x = -1.870977678 + 5.402650355 Combine like terms: -5.402650355 + 5.402650355 = 0.000000000 0.000000000 + x = -1.870977678 + 5.402650355 x = -1.870977678 + 5.402650355 Combine like terms: -1.870977678 + 5.402650355 = 3.531672677 x = 3.531672677 Simplifying x = 3.531672677Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.273628033, 3.531672677}
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