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Simplifying 4x2 + 3x + -170368 = 0 Reorder the terms: -170368 + 3x + 4x2 = 0 Solving -170368 + 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'. -42592 + 0.75x + x2 = 0 Move the constant term to the right: Add '42592' to each side of the equation. -42592 + 0.75x + 42592 + x2 = 0 + 42592 Reorder the terms: -42592 + 42592 + 0.75x + x2 = 0 + 42592 Combine like terms: -42592 + 42592 = 0 0 + 0.75x + x2 = 0 + 42592 0.75x + x2 = 0 + 42592 Combine like terms: 0 + 42592 = 42592 0.75x + x2 = 42592 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 = 42592 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 42592 + 0.140625 Combine like terms: 42592 + 0.140625 = 42592.140625 0.140625 + 0.75x + x2 = 42592.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 42592.140625 Calculate the square root of the right side: 206.378634129 Break this problem into two subproblems by setting (x + 0.375) equal to 206.378634129 and -206.378634129.Subproblem 1
x + 0.375 = 206.378634129 Simplifying x + 0.375 = 206.378634129 Reorder the terms: 0.375 + x = 206.378634129 Solving 0.375 + x = 206.378634129 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 = 206.378634129 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 206.378634129 + -0.375 x = 206.378634129 + -0.375 Combine like terms: 206.378634129 + -0.375 = 206.003634129 x = 206.003634129 Simplifying x = 206.003634129Subproblem 2
x + 0.375 = -206.378634129 Simplifying x + 0.375 = -206.378634129 Reorder the terms: 0.375 + x = -206.378634129 Solving 0.375 + x = -206.378634129 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 = -206.378634129 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -206.378634129 + -0.375 x = -206.378634129 + -0.375 Combine like terms: -206.378634129 + -0.375 = -206.753634129 x = -206.753634129 Simplifying x = -206.753634129Solution
The solution to the problem is based on the solutions from the subproblems. x = {206.003634129, -206.753634129}
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