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Simplifying 4x2 + 43x + 35 = 0 Reorder the terms: 35 + 43x + 4x2 = 0 Solving 35 + 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'. 8.75 + 10.75x + x2 = 0 Move the constant term to the right: Add '-8.75' to each side of the equation. 8.75 + 10.75x + -8.75 + x2 = 0 + -8.75 Reorder the terms: 8.75 + -8.75 + 10.75x + x2 = 0 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + 10.75x + x2 = 0 + -8.75 10.75x + x2 = 0 + -8.75 Combine like terms: 0 + -8.75 = -8.75 10.75x + x2 = -8.75 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 = -8.75 + 28.890625 Reorder the terms: 28.890625 + 10.75x + x2 = -8.75 + 28.890625 Combine like terms: -8.75 + 28.890625 = 20.140625 28.890625 + 10.75x + x2 = 20.140625 Factor a perfect square on the left side: (x + 5.375)(x + 5.375) = 20.140625 Calculate the square root of the right side: 4.487830768 Break this problem into two subproblems by setting (x + 5.375) equal to 4.487830768 and -4.487830768.Subproblem 1
x + 5.375 = 4.487830768 Simplifying x + 5.375 = 4.487830768 Reorder the terms: 5.375 + x = 4.487830768 Solving 5.375 + x = 4.487830768 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 = 4.487830768 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = 4.487830768 + -5.375 x = 4.487830768 + -5.375 Combine like terms: 4.487830768 + -5.375 = -0.887169232 x = -0.887169232 Simplifying x = -0.887169232Subproblem 2
x + 5.375 = -4.487830768 Simplifying x + 5.375 = -4.487830768 Reorder the terms: 5.375 + x = -4.487830768 Solving 5.375 + x = -4.487830768 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 = -4.487830768 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = -4.487830768 + -5.375 x = -4.487830768 + -5.375 Combine like terms: -4.487830768 + -5.375 = -9.862830768 x = -9.862830768 Simplifying x = -9.862830768Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.887169232, -9.862830768}
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