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Simplifying 4x2 + 3x + -729 = 0 Reorder the terms: -729 + 3x + 4x2 = 0 Solving -729 + 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'. -182.25 + 0.75x + x2 = 0 Move the constant term to the right: Add '182.25' to each side of the equation. -182.25 + 0.75x + 182.25 + x2 = 0 + 182.25 Reorder the terms: -182.25 + 182.25 + 0.75x + x2 = 0 + 182.25 Combine like terms: -182.25 + 182.25 = 0.00 0.00 + 0.75x + x2 = 0 + 182.25 0.75x + x2 = 0 + 182.25 Combine like terms: 0 + 182.25 = 182.25 0.75x + x2 = 182.25 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 = 182.25 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 182.25 + 0.140625 Combine like terms: 182.25 + 0.140625 = 182.390625 0.140625 + 0.75x + x2 = 182.390625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 182.390625 Calculate the square root of the right side: 13.505207329 Break this problem into two subproblems by setting (x + 0.375) equal to 13.505207329 and -13.505207329.Subproblem 1
x + 0.375 = 13.505207329 Simplifying x + 0.375 = 13.505207329 Reorder the terms: 0.375 + x = 13.505207329 Solving 0.375 + x = 13.505207329 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 = 13.505207329 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 13.505207329 + -0.375 x = 13.505207329 + -0.375 Combine like terms: 13.505207329 + -0.375 = 13.130207329 x = 13.130207329 Simplifying x = 13.130207329Subproblem 2
x + 0.375 = -13.505207329 Simplifying x + 0.375 = -13.505207329 Reorder the terms: 0.375 + x = -13.505207329 Solving 0.375 + x = -13.505207329 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 = -13.505207329 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -13.505207329 + -0.375 x = -13.505207329 + -0.375 Combine like terms: -13.505207329 + -0.375 = -13.880207329 x = -13.880207329 Simplifying x = -13.880207329Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.130207329, -13.880207329}
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