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Simplifying 4x2 + 35x + -37 = 0 Reorder the terms: -37 + 35x + 4x2 = 0 Solving -37 + 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'. -9.25 + 8.75x + x2 = 0 Move the constant term to the right: Add '9.25' to each side of the equation. -9.25 + 8.75x + 9.25 + x2 = 0 + 9.25 Reorder the terms: -9.25 + 9.25 + 8.75x + x2 = 0 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + 8.75x + x2 = 0 + 9.25 8.75x + x2 = 0 + 9.25 Combine like terms: 0 + 9.25 = 9.25 8.75x + x2 = 9.25 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 = 9.25 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = 9.25 + 19.140625 Combine like terms: 9.25 + 19.140625 = 28.390625 19.140625 + 8.75x + x2 = 28.390625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 28.390625 Calculate the square root of the right side: 5.328285371 Break this problem into two subproblems by setting (x + 4.375) equal to 5.328285371 and -5.328285371.Subproblem 1
x + 4.375 = 5.328285371 Simplifying x + 4.375 = 5.328285371 Reorder the terms: 4.375 + x = 5.328285371 Solving 4.375 + x = 5.328285371 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 = 5.328285371 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 5.328285371 + -4.375 x = 5.328285371 + -4.375 Combine like terms: 5.328285371 + -4.375 = 0.953285371 x = 0.953285371 Simplifying x = 0.953285371Subproblem 2
x + 4.375 = -5.328285371 Simplifying x + 4.375 = -5.328285371 Reorder the terms: 4.375 + x = -5.328285371 Solving 4.375 + x = -5.328285371 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 = -5.328285371 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -5.328285371 + -4.375 x = -5.328285371 + -4.375 Combine like terms: -5.328285371 + -4.375 = -9.703285371 x = -9.703285371 Simplifying x = -9.703285371Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.953285371, -9.703285371}
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