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Simplifying 4x2 + 35x + 64 = 0 Reorder the terms: 64 + 35x + 4x2 = 0 Solving 64 + 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'. 16 + 8.75x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + 8.75x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 8.75x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 8.75x + x2 = 0 + -16 8.75x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 8.75x + x2 = -16 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 = -16 + 19.140625 Reorder the terms: 19.140625 + 8.75x + x2 = -16 + 19.140625 Combine like terms: -16 + 19.140625 = 3.140625 19.140625 + 8.75x + x2 = 3.140625 Factor a perfect square on the left side: (x + 4.375)(x + 4.375) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + 4.375) equal to 1.77218086 and -1.77218086.Subproblem 1
x + 4.375 = 1.77218086 Simplifying x + 4.375 = 1.77218086 Reorder the terms: 4.375 + x = 1.77218086 Solving 4.375 + x = 1.77218086 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 = 1.77218086 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = 1.77218086 + -4.375 x = 1.77218086 + -4.375 Combine like terms: 1.77218086 + -4.375 = -2.60281914 x = -2.60281914 Simplifying x = -2.60281914Subproblem 2
x + 4.375 = -1.77218086 Simplifying x + 4.375 = -1.77218086 Reorder the terms: 4.375 + x = -1.77218086 Solving 4.375 + x = -1.77218086 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 = -1.77218086 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + x = -1.77218086 + -4.375 x = -1.77218086 + -4.375 Combine like terms: -1.77218086 + -4.375 = -6.14718086 x = -6.14718086 Simplifying x = -6.14718086Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.60281914, -6.14718086}
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