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Simplifying 4x2 + -67x + -289 = 0 Reorder the terms: -289 + -67x + 4x2 = 0 Solving -289 + -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'. -72.25 + -16.75x + x2 = 0 Move the constant term to the right: Add '72.25' to each side of the equation. -72.25 + -16.75x + 72.25 + x2 = 0 + 72.25 Reorder the terms: -72.25 + 72.25 + -16.75x + x2 = 0 + 72.25 Combine like terms: -72.25 + 72.25 = 0.00 0.00 + -16.75x + x2 = 0 + 72.25 -16.75x + x2 = 0 + 72.25 Combine like terms: 0 + 72.25 = 72.25 -16.75x + x2 = 72.25 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 = 72.25 + 70.140625 Reorder the terms: 70.140625 + -16.75x + x2 = 72.25 + 70.140625 Combine like terms: 72.25 + 70.140625 = 142.390625 70.140625 + -16.75x + x2 = 142.390625 Factor a perfect square on the left side: (x + -8.375)(x + -8.375) = 142.390625 Calculate the square root of the right side: 11.932754292 Break this problem into two subproblems by setting (x + -8.375) equal to 11.932754292 and -11.932754292.Subproblem 1
x + -8.375 = 11.932754292 Simplifying x + -8.375 = 11.932754292 Reorder the terms: -8.375 + x = 11.932754292 Solving -8.375 + x = 11.932754292 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 = 11.932754292 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = 11.932754292 + 8.375 x = 11.932754292 + 8.375 Combine like terms: 11.932754292 + 8.375 = 20.307754292 x = 20.307754292 Simplifying x = 20.307754292Subproblem 2
x + -8.375 = -11.932754292 Simplifying x + -8.375 = -11.932754292 Reorder the terms: -8.375 + x = -11.932754292 Solving -8.375 + x = -11.932754292 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 = -11.932754292 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = -11.932754292 + 8.375 x = -11.932754292 + 8.375 Combine like terms: -11.932754292 + 8.375 = -3.557754292 x = -3.557754292 Simplifying x = -3.557754292Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.307754292, -3.557754292}
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