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Simplifying 4x2 + -67x + -287 = 0 Reorder the terms: -287 + -67x + 4x2 = 0 Solving -287 + -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'. -71.75 + -16.75x + x2 = 0 Move the constant term to the right: Add '71.75' to each side of the equation. -71.75 + -16.75x + 71.75 + x2 = 0 + 71.75 Reorder the terms: -71.75 + 71.75 + -16.75x + x2 = 0 + 71.75 Combine like terms: -71.75 + 71.75 = 0.00 0.00 + -16.75x + x2 = 0 + 71.75 -16.75x + x2 = 0 + 71.75 Combine like terms: 0 + 71.75 = 71.75 -16.75x + x2 = 71.75 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 = 71.75 + 70.140625 Reorder the terms: 70.140625 + -16.75x + x2 = 71.75 + 70.140625 Combine like terms: 71.75 + 70.140625 = 141.890625 70.140625 + -16.75x + x2 = 141.890625 Factor a perfect square on the left side: (x + -8.375)(x + -8.375) = 141.890625 Calculate the square root of the right side: 11.911785131 Break this problem into two subproblems by setting (x + -8.375) equal to 11.911785131 and -11.911785131.Subproblem 1
x + -8.375 = 11.911785131 Simplifying x + -8.375 = 11.911785131 Reorder the terms: -8.375 + x = 11.911785131 Solving -8.375 + x = 11.911785131 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 = 11.911785131 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = 11.911785131 + 8.375 x = 11.911785131 + 8.375 Combine like terms: 11.911785131 + 8.375 = 20.286785131 x = 20.286785131 Simplifying x = 20.286785131Subproblem 2
x + -8.375 = -11.911785131 Simplifying x + -8.375 = -11.911785131 Reorder the terms: -8.375 + x = -11.911785131 Solving -8.375 + x = -11.911785131 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 = -11.911785131 + 8.375 Combine like terms: -8.375 + 8.375 = 0.000 0.000 + x = -11.911785131 + 8.375 x = -11.911785131 + 8.375 Combine like terms: -11.911785131 + 8.375 = -3.536785131 x = -3.536785131 Simplifying x = -3.536785131Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.286785131, -3.536785131}
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