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Simplifying 12x2 + 105x + 147 = 35 Reorder the terms: 147 + 105x + 12x2 = 35 Solving 147 + 105x + 12x2 = 35 Solving for variable 'x'. Reorder the terms: 147 + -35 + 105x + 12x2 = 35 + -35 Combine like terms: 147 + -35 = 112 112 + 105x + 12x2 = 35 + -35 Combine like terms: 35 + -35 = 0 112 + 105x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 9.333333333 + 8.75x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + 8.75x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + 8.75x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + 8.75x + x2 = 0 + -9.333333333 8.75x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 8.75x + x2 = -9.333333333 The x term is 8.75x. Take half its coefficient (4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. 8.75x + 19.140625 + x2 = -9.333333333 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -9.333333333 + 19.140625 Combine like terms: -9.333333333 + 19.140625 = 9.807291667 19.140625 + 8.75x + x2 = 9.807291667 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 9.807291667 Calculate the square root of the right side: 3.131659571 Break this problem into two subproblems by setting (x + 4.375) equal to 3.131659571 and -3.131659571.Subproblem 1
x + 4.375 = 3.131659571 Simplifying x + 4.375 = 3.131659571 Reorder the terms: 4.375 + x = 3.131659571 Solving 4.375 + x = 3.131659571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = 3.131659571 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 3.131659571 + -4.375 x = 3.131659571 + -4.375 Combine like terms: 3.131659571 + -4.375 = -1.243340429 x = -1.243340429 Simplifying x = -1.243340429Subproblem 2
x + 4.375 = -3.131659571 Simplifying x + 4.375 = -3.131659571 Reorder the terms: 4.375 + x = -3.131659571 Solving 4.375 + x = -3.131659571 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.375' to each side of the equation. 4.375 + -4.375 + x = -3.131659571 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -3.131659571 + -4.375 x = -3.131659571 + -4.375 Combine like terms: -3.131659571 + -4.375 = -7.506659571 x = -7.506659571 Simplifying x = -7.506659571Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.243340429, -7.506659571}
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