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Simplifying 4.905x2 + -272x + 960 = 0 Reorder the terms: 960 + -272x + 4.905x2 = 0 Solving 960 + -272x + 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'. 195.7186544 + -55.45361876x + x2 = 0 Move the constant term to the right: Add '-195.7186544' to each side of the equation. 195.7186544 + -55.45361876x + -195.7186544 + x2 = 0 + -195.7186544 Reorder the terms: 195.7186544 + -195.7186544 + -55.45361876x + x2 = 0 + -195.7186544 Combine like terms: 195.7186544 + -195.7186544 = 0.0000000 0.0000000 + -55.45361876x + x2 = 0 + -195.7186544 -55.45361876x + x2 = 0 + -195.7186544 Combine like terms: 0 + -195.7186544 = -195.7186544 -55.45361876x + x2 = -195.7186544 The x term is -55.45361876x. Take half its coefficient (-27.72680938). Square it (768.7759584) and add it to both sides. Add '768.7759584' to each side of the equation. -55.45361876x + 768.7759584 + x2 = -195.7186544 + 768.7759584 Reorder the terms: 768.7759584 + -55.45361876x + x2 = -195.7186544 + 768.7759584 Combine like terms: -195.7186544 + 768.7759584 = 573.057304 768.7759584 + -55.45361876x + x2 = 573.057304 Factor a perfect square on the left side: (x + -27.72680938)(x + -27.72680938) = 573.057304 Calculate the square root of the right side: 23.938615332 Break this problem into two subproblems by setting (x + -27.72680938) equal to 23.938615332 and -23.938615332.Subproblem 1
x + -27.72680938 = 23.938615332 Simplifying x + -27.72680938 = 23.938615332 Reorder the terms: -27.72680938 + x = 23.938615332 Solving -27.72680938 + x = 23.938615332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.72680938' to each side of the equation. -27.72680938 + 27.72680938 + x = 23.938615332 + 27.72680938 Combine like terms: -27.72680938 + 27.72680938 = 0.00000000 0.00000000 + x = 23.938615332 + 27.72680938 x = 23.938615332 + 27.72680938 Combine like terms: 23.938615332 + 27.72680938 = 51.665424712 x = 51.665424712 Simplifying x = 51.665424712Subproblem 2
x + -27.72680938 = -23.938615332 Simplifying x + -27.72680938 = -23.938615332 Reorder the terms: -27.72680938 + x = -23.938615332 Solving -27.72680938 + x = -23.938615332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '27.72680938' to each side of the equation. -27.72680938 + 27.72680938 + x = -23.938615332 + 27.72680938 Combine like terms: -27.72680938 + 27.72680938 = 0.00000000 0.00000000 + x = -23.938615332 + 27.72680938 x = -23.938615332 + 27.72680938 Combine like terms: -23.938615332 + 27.72680938 = 3.788194048 x = 3.788194048 Simplifying x = 3.788194048Solution
The solution to the problem is based on the solutions from the subproblems. x = {51.665424712, 3.788194048}
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