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Simplifying 4x2 + 43x + -108 = 0 Reorder the terms: -108 + 43x + 4x2 = 0 Solving -108 + 43x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -27 + 10.75x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 10.75x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 10.75x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 10.75x + x2 = 0 + 27 10.75x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 10.75x + x2 = 27 The x term is 10.75x. Take half its coefficient (5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. 10.75x + 28.890625 + x2 = 27 + 28.890625 Reorder the terms: 28.890625 + 10.75x + x2 = 27 + 28.890625 Combine like terms: 27 + 28.890625 = 55.890625 28.890625 + 10.75x + x2 = 55.890625 Factor a perfect square on the left side: (x + 5.375)(x + 5.375) = 55.890625 Calculate the square root of the right side: 7.476003277 Break this problem into two subproblems by setting (x + 5.375) equal to 7.476003277 and -7.476003277.Subproblem 1
x + 5.375 = 7.476003277 Simplifying x + 5.375 = 7.476003277 Reorder the terms: 5.375 + x = 7.476003277 Solving 5.375 + x = 7.476003277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = 7.476003277 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = 7.476003277 + -5.375 x = 7.476003277 + -5.375 Combine like terms: 7.476003277 + -5.375 = 2.101003277 x = 2.101003277 Simplifying x = 2.101003277Subproblem 2
x + 5.375 = -7.476003277 Simplifying x + 5.375 = -7.476003277 Reorder the terms: 5.375 + x = -7.476003277 Solving 5.375 + x = -7.476003277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = -7.476003277 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = -7.476003277 + -5.375 x = -7.476003277 + -5.375 Combine like terms: -7.476003277 + -5.375 = -12.851003277 x = -12.851003277 Simplifying x = -12.851003277Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.101003277, -12.851003277}
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