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Simplifying 0 = -16.75x2 + 100.5x + -2.75 Reorder the terms: 0 = -2.75 + 100.5x + -16.75x2 Solving 0 = -2.75 + 100.5x + -16.75x2 Solving for variable 'x'. Combine like terms: 0 + 2.75 = 2.75 2.75 + -100.5x + 16.75x2 = -2.75 + 100.5x + -16.75x2 + 2.75 + -100.5x + 16.75x2 Reorder the terms: 2.75 + -100.5x + 16.75x2 = -2.75 + 2.75 + 100.5x + -100.5x + -16.75x2 + 16.75x2 Combine like terms: -2.75 + 2.75 = 0.00 2.75 + -100.5x + 16.75x2 = 0.00 + 100.5x + -100.5x + -16.75x2 + 16.75x2 2.75 + -100.5x + 16.75x2 = 100.5x + -100.5x + -16.75x2 + 16.75x2 Combine like terms: 100.5x + -100.5x = 0.0 2.75 + -100.5x + 16.75x2 = 0.0 + -16.75x2 + 16.75x2 2.75 + -100.5x + 16.75x2 = -16.75x2 + 16.75x2 Combine like terms: -16.75x2 + 16.75x2 = 0.00 2.75 + -100.5x + 16.75x2 = 0.00 Begin completing the square. Divide all terms by 16.75 the coefficient of the squared term: Divide each side by '16.75'. 0.1641791045 + -6x + x2 = 0 Move the constant term to the right: Add '-0.1641791045' to each side of the equation. 0.1641791045 + -6x + -0.1641791045 + x2 = 0 + -0.1641791045 Reorder the terms: 0.1641791045 + -0.1641791045 + -6x + x2 = 0 + -0.1641791045 Combine like terms: 0.1641791045 + -0.1641791045 = 0.0000000000 0.0000000000 + -6x + x2 = 0 + -0.1641791045 -6x + x2 = 0 + -0.1641791045 Combine like terms: 0 + -0.1641791045 = -0.1641791045 -6x + x2 = -0.1641791045 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -0.1641791045 + 9 Reorder the terms: 9 + -6x + x2 = -0.1641791045 + 9 Combine like terms: -0.1641791045 + 9 = 8.8358208955 9 + -6x + x2 = 8.8358208955 Factor a perfect square on the left side: (x + -3)(x + -3) = 8.8358208955 Calculate the square root of the right side: 2.972510874 Break this problem into two subproblems by setting (x + -3) equal to 2.972510874 and -2.972510874.Subproblem 1
x + -3 = 2.972510874 Simplifying x + -3 = 2.972510874 Reorder the terms: -3 + x = 2.972510874 Solving -3 + x = 2.972510874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.972510874 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.972510874 + 3 x = 2.972510874 + 3 Combine like terms: 2.972510874 + 3 = 5.972510874 x = 5.972510874 Simplifying x = 5.972510874Subproblem 2
x + -3 = -2.972510874 Simplifying x + -3 = -2.972510874 Reorder the terms: -3 + x = -2.972510874 Solving -3 + x = -2.972510874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.972510874 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.972510874 + 3 x = -2.972510874 + 3 Combine like terms: -2.972510874 + 3 = 0.027489126 x = 0.027489126 Simplifying x = 0.027489126Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.972510874, 0.027489126}
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