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Simplifying 3x2 + 2.25x + -48.18 = 0 Reorder the terms: -48.18 + 2.25x + 3x2 = 0 Solving -48.18 + 2.25x + 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'. -16.06 + 0.75x + x2 = 0 Move the constant term to the right: Add '16.06' to each side of the equation. -16.06 + 0.75x + 16.06 + x2 = 0 + 16.06 Reorder the terms: -16.06 + 16.06 + 0.75x + x2 = 0 + 16.06 Combine like terms: -16.06 + 16.06 = 0.00 0.00 + 0.75x + x2 = 0 + 16.06 0.75x + x2 = 0 + 16.06 Combine like terms: 0 + 16.06 = 16.06 0.75x + x2 = 16.06 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 16.06 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 16.06 + 0.140625 Combine like terms: 16.06 + 0.140625 = 16.200625 0.140625 + 0.75x + x2 = 16.200625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 16.200625 Calculate the square root of the right side: 4.025 Break this problem into two subproblems by setting (x + 0.375) equal to 4.025 and -4.025.Subproblem 1
x + 0.375 = 4.025 Simplifying x + 0.375 = 4.025 Reorder the terms: 0.375 + x = 4.025 Solving 0.375 + x = 4.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 4.025 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 4.025 + -0.375 x = 4.025 + -0.375 Combine like terms: 4.025 + -0.375 = 3.65 x = 3.65 Simplifying x = 3.65Subproblem 2
x + 0.375 = -4.025 Simplifying x + 0.375 = -4.025 Reorder the terms: 0.375 + x = -4.025 Solving 0.375 + x = -4.025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -4.025 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -4.025 + -0.375 x = -4.025 + -0.375 Combine like terms: -4.025 + -0.375 = -4.4 x = -4.4 Simplifying x = -4.4Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.65, -4.4}
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