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Simplifying 16x2 + -48x + 9 = 0 Reorder the terms: 9 + -48x + 16x2 = 0 Solving 9 + -48x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 0.5625 + -3x + x2 = 0 Move the constant term to the right: Add '-0.5625' to each side of the equation. 0.5625 + -3x + -0.5625 + x2 = 0 + -0.5625 Reorder the terms: 0.5625 + -0.5625 + -3x + x2 = 0 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + -3x + x2 = 0 + -0.5625 -3x + x2 = 0 + -0.5625 Combine like terms: 0 + -0.5625 = -0.5625 -3x + x2 = -0.5625 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.5625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.5625 + 2.25 Combine like terms: -0.5625 + 2.25 = 1.6875 2.25 + -3x + x2 = 1.6875 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.6875 Calculate the square root of the right side: 1.299038106 Break this problem into two subproblems by setting (x + -1.5) equal to 1.299038106 and -1.299038106.Subproblem 1
x + -1.5 = 1.299038106 Simplifying x + -1.5 = 1.299038106 Reorder the terms: -1.5 + x = 1.299038106 Solving -1.5 + x = 1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.299038106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.299038106 + 1.5 x = 1.299038106 + 1.5 Combine like terms: 1.299038106 + 1.5 = 2.799038106 x = 2.799038106 Simplifying x = 2.799038106Subproblem 2
x + -1.5 = -1.299038106 Simplifying x + -1.5 = -1.299038106 Reorder the terms: -1.5 + x = -1.299038106 Solving -1.5 + x = -1.299038106 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.299038106 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.299038106 + 1.5 x = -1.299038106 + 1.5 Combine like terms: -1.299038106 + 1.5 = 0.200961894 x = 0.200961894 Simplifying x = 0.200961894Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.799038106, 0.200961894}
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