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Simplifying 4x2 + 3x + -35 = 0 Reorder the terms: -35 + 3x + 4x2 = 0 Solving -35 + 3x + 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 + 0.75x + x2 = 0 Move the constant term to the right: Add '8.75' to each side of the equation. -8.75 + 0.75x + 8.75 + x2 = 0 + 8.75 Reorder the terms: -8.75 + 8.75 + 0.75x + x2 = 0 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + 0.75x + x2 = 0 + 8.75 0.75x + x2 = 0 + 8.75 Combine like terms: 0 + 8.75 = 8.75 0.75x + x2 = 8.75 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 8.75 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 8.75 + 0.140625 Combine like terms: 8.75 + 0.140625 = 8.890625 0.140625 + 0.75x + x2 = 8.890625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 8.890625 Calculate the square root of the right side: 2.98171511 Break this problem into two subproblems by setting (x + 0.375) equal to 2.98171511 and -2.98171511.Subproblem 1
x + 0.375 = 2.98171511 Simplifying x + 0.375 = 2.98171511 Reorder the terms: 0.375 + x = 2.98171511 Solving 0.375 + x = 2.98171511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 2.98171511 + -0.375 x = 2.98171511 + -0.375 Combine like terms: 2.98171511 + -0.375 = 2.60671511 x = 2.60671511 Simplifying x = 2.60671511Subproblem 2
x + 0.375 = -2.98171511 Simplifying x + 0.375 = -2.98171511 Reorder the terms: 0.375 + x = -2.98171511 Solving 0.375 + x = -2.98171511 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -2.98171511 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -2.98171511 + -0.375 x = -2.98171511 + -0.375 Combine like terms: -2.98171511 + -0.375 = -3.35671511 x = -3.35671511 Simplifying x = -3.35671511Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.60671511, -3.35671511}
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