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Simplifying 4x2 + 67x + -334 = 0 Reorder the terms: -334 + 67x + 4x2 = 0 Solving -334 + 67x + 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'. -83.5 + 16.75x + x2 = 0 Move the constant term to the right: Add '83.5' to each side of the equation. -83.5 + 16.75x + 83.5 + x2 = 0 + 83.5 Reorder the terms: -83.5 + 83.5 + 16.75x + x2 = 0 + 83.5 Combine like terms: -83.5 + 83.5 = 0.0 0.0 + 16.75x + x2 = 0 + 83.5 16.75x + x2 = 0 + 83.5 Combine like terms: 0 + 83.5 = 83.5 16.75x + x2 = 83.5 The x term is 16.75x. Take half its coefficient (8.375). Square it (70.140625) and add it to both sides. Add '70.140625' to each side of the equation. 16.75x + 70.140625 + x2 = 83.5 + 70.140625 Reorder the terms: 70.140625 + 16.75x + x2 = 83.5 + 70.140625 Combine like terms: 83.5 + 70.140625 = 153.640625 70.140625 + 16.75x + x2 = 153.640625 Factor a perfect square on the left side: (x + 8.375)(x + 8.375) = 153.640625 Calculate the square root of the right side: 12.395185557 Break this problem into two subproblems by setting (x + 8.375) equal to 12.395185557 and -12.395185557.Subproblem 1
x + 8.375 = 12.395185557 Simplifying x + 8.375 = 12.395185557 Reorder the terms: 8.375 + x = 12.395185557 Solving 8.375 + x = 12.395185557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = 12.395185557 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = 12.395185557 + -8.375 x = 12.395185557 + -8.375 Combine like terms: 12.395185557 + -8.375 = 4.020185557 x = 4.020185557 Simplifying x = 4.020185557Subproblem 2
x + 8.375 = -12.395185557 Simplifying x + 8.375 = -12.395185557 Reorder the terms: 8.375 + x = -12.395185557 Solving 8.375 + x = -12.395185557 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.375' to each side of the equation. 8.375 + -8.375 + x = -12.395185557 + -8.375 Combine like terms: 8.375 + -8.375 = 0.000 0.000 + x = -12.395185557 + -8.375 x = -12.395185557 + -8.375 Combine like terms: -12.395185557 + -8.375 = -20.770185557 x = -20.770185557 Simplifying x = -20.770185557Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.020185557, -20.770185557}
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