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Simplifying 4(x2) + -35x + -3 = 0 Reorder the terms: -3 + -35x + 4x2 = 0 Solving -3 + -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'. -0.75 + -8.75x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -8.75x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -8.75x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -8.75x + x2 = 0 + 0.75 -8.75x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -8.75x + x2 = 0.75 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 = 0.75 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 0.75 + 19.140625 Combine like terms: 0.75 + 19.140625 = 19.890625 19.140625 + -8.75x + x2 = 19.890625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 19.890625 Calculate the square root of the right side: 4.459890694 Break this problem into two subproblems by setting (x + -4.375) equal to 4.459890694 and -4.459890694.Subproblem 1
x + -4.375 = 4.459890694 Simplifying x + -4.375 = 4.459890694 Reorder the terms: -4.375 + x = 4.459890694 Solving -4.375 + x = 4.459890694 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 = 4.459890694 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 4.459890694 + 4.375 x = 4.459890694 + 4.375 Combine like terms: 4.459890694 + 4.375 = 8.834890694 x = 8.834890694 Simplifying x = 8.834890694Subproblem 2
x + -4.375 = -4.459890694 Simplifying x + -4.375 = -4.459890694 Reorder the terms: -4.375 + x = -4.459890694 Solving -4.375 + x = -4.459890694 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 = -4.459890694 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -4.459890694 + 4.375 x = -4.459890694 + 4.375 Combine like terms: -4.459890694 + 4.375 = -0.084890694 x = -0.084890694 Simplifying x = -0.084890694Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.834890694, -0.084890694}
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