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Simplifying 4x2 + -35x + -35 = 0 Reorder the terms: -35 + -35x + 4x2 = 0 Solving -35 + -35x + 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 + -8.75x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + -8.75x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + -8.75x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + -8.75x + x2 = 0 + 8.75 -8.75x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 -8.75x + x2 = 8.75 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 = 8.75 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 8.75 + 19.140625 Combine like terms: 8.75 + 19.140625 = 27.890625 19.140625 + -8.75x + x2 = 27.890625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 27.890625 Calculate the square root of the right side: 5.281157544 Break this problem into two subproblems by setting (x + -4.375) equal to 5.281157544 and -5.281157544.Subproblem 1
x + -4.375 = 5.281157544 Simplifying x + -4.375 = 5.281157544 Reorder the terms: -4.375 + x = 5.281157544 Solving -4.375 + x = 5.281157544 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 = 5.281157544 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 5.281157544 + 4.375 x = 5.281157544 + 4.375 Combine like terms: 5.281157544 + 4.375 = 9.656157544 x = 9.656157544 Simplifying x = 9.656157544Subproblem 2
x + -4.375 = -5.281157544 Simplifying x + -4.375 = -5.281157544 Reorder the terms: -4.375 + x = -5.281157544 Solving -4.375 + x = -5.281157544 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 = -5.281157544 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -5.281157544 + 4.375 x = -5.281157544 + 4.375 Combine like terms: -5.281157544 + 4.375 = -0.906157544 x = -0.906157544 Simplifying x = -0.906157544Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.656157544, -0.906157544}
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