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Simplifying 4x2 + -35x = 49 Reorder the terms: -35x + 4x2 = 49 Solving -35x + 4x2 = 49 Solving for variable 'x'. Reorder the terms: -49 + -35x + 4x2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -35x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -8.75x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -8.75x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -8.75x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -8.75x + x2 = 0 + 12.25 -8.75x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -8.75x + x2 = 12.25 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 = 12.25 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 12.25 + 19.140625 Combine like terms: 12.25 + 19.140625 = 31.390625 19.140625 + -8.75x + x2 = 31.390625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 31.390625 Calculate the square root of the right side: 5.602733708 Break this problem into two subproblems by setting (x + -4.375) equal to 5.602733708 and -5.602733708.Subproblem 1
x + -4.375 = 5.602733708 Simplifying x + -4.375 = 5.602733708 Reorder the terms: -4.375 + x = 5.602733708 Solving -4.375 + x = 5.602733708 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 = 5.602733708 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 5.602733708 + 4.375 x = 5.602733708 + 4.375 Combine like terms: 5.602733708 + 4.375 = 9.977733708 x = 9.977733708 Simplifying x = 9.977733708Subproblem 2
x + -4.375 = -5.602733708 Simplifying x + -4.375 = -5.602733708 Reorder the terms: -4.375 + x = -5.602733708 Solving -4.375 + x = -5.602733708 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 = -5.602733708 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -5.602733708 + 4.375 x = -5.602733708 + 4.375 Combine like terms: -5.602733708 + 4.375 = -1.227733708 x = -1.227733708 Simplifying x = -1.227733708Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.977733708, -1.227733708}
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