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Simplifying 0.25x2 + -1x + -17 = 0 Reorder the terms: -17 + -1x + 0.25x2 = 0 Solving -17 + -1x + 0.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -68 + -4x + x2 = 0 Move the constant term to the right: Add '68' to each side of the equation. -68 + -4x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + -4x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + -4x + x2 = 0 + 68 -4x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 -4x + x2 = 68 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 68 + 4 Reorder the terms: 4 + -4x + x2 = 68 + 4 Combine like terms: 68 + 4 = 72 4 + -4x + x2 = 72 Factor a perfect square on the left side: (x + -2)(x + -2) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (x + -2) equal to 8.485281374 and -8.485281374.Subproblem 1
x + -2 = 8.485281374 Simplifying x + -2 = 8.485281374 Reorder the terms: -2 + x = 8.485281374 Solving -2 + x = 8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 8.485281374 + 2 Combine like terms: -2 + 2 = 0 0 + x = 8.485281374 + 2 x = 8.485281374 + 2 Combine like terms: 8.485281374 + 2 = 10.485281374 x = 10.485281374 Simplifying x = 10.485281374Subproblem 2
x + -2 = -8.485281374 Simplifying x + -2 = -8.485281374 Reorder the terms: -2 + x = -8.485281374 Solving -2 + x = -8.485281374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -8.485281374 + 2 Combine like terms: -2 + 2 = 0 0 + x = -8.485281374 + 2 x = -8.485281374 + 2 Combine like terms: -8.485281374 + 2 = -6.485281374 x = -6.485281374 Simplifying x = -6.485281374Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.485281374, -6.485281374}
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