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Simplifying 2x2 + 1.5x + 17 = 43 Reorder the terms: 17 + 1.5x + 2x2 = 43 Solving 17 + 1.5x + 2x2 = 43 Solving for variable 'x'. Reorder the terms: 17 + -43 + 1.5x + 2x2 = 43 + -43 Combine like terms: 17 + -43 = -26 -26 + 1.5x + 2x2 = 43 + -43 Combine like terms: 43 + -43 = 0 -26 + 1.5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -13 + 0.75x + x2 = 0 Move the constant term to the right: Add '13' to each side of the equation. -13 + 0.75x + 13 + x2 = 0 + 13 Reorder the terms: -13 + 13 + 0.75x + x2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 0.75x + x2 = 0 + 13 0.75x + x2 = 0 + 13 Combine like terms: 0 + 13 = 13 0.75x + x2 = 13 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 = 13 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 13 + 0.140625 Combine like terms: 13 + 0.140625 = 13.140625 0.140625 + 0.75x + x2 = 13.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 13.140625 Calculate the square root of the right side: 3.625 Break this problem into two subproblems by setting (x + 0.375) equal to 3.625 and -3.625.Subproblem 1
x + 0.375 = 3.625 Simplifying x + 0.375 = 3.625 Reorder the terms: 0.375 + x = 3.625 Solving 0.375 + x = 3.625 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 = 3.625 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 3.625 + -0.375 x = 3.625 + -0.375 Combine like terms: 3.625 + -0.375 = 3.25 x = 3.25 Simplifying x = 3.25Subproblem 2
x + 0.375 = -3.625 Simplifying x + 0.375 = -3.625 Reorder the terms: 0.375 + x = -3.625 Solving 0.375 + x = -3.625 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 = -3.625 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -3.625 + -0.375 x = -3.625 + -0.375 Combine like terms: -3.625 + -0.375 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.25, -4}
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