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Simplifying -1x2 + 12x = -17 Reorder the terms: 12x + -1x2 = -17 Solving 12x + -1x2 = -17 Solving for variable 'x'. Reorder the terms: 17 + 12x + -1x2 = -17 + 17 Combine like terms: -17 + 17 = 0 17 + 12x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -17 + -12x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -12x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -12x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -12x + x2 = 0 + 17 -12x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -12x + x2 = 17 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 17 + 36 Reorder the terms: 36 + -12x + x2 = 17 + 36 Combine like terms: 17 + 36 = 53 36 + -12x + x2 = 53 Factor a perfect square on the left side: (x + -6)(x + -6) = 53 Calculate the square root of the right side: 7.280109889 Break this problem into two subproblems by setting (x + -6) equal to 7.280109889 and -7.280109889.Subproblem 1
x + -6 = 7.280109889 Simplifying x + -6 = 7.280109889 Reorder the terms: -6 + x = 7.280109889 Solving -6 + x = 7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.280109889 + 6 x = 7.280109889 + 6 Combine like terms: 7.280109889 + 6 = 13.280109889 x = 13.280109889 Simplifying x = 13.280109889Subproblem 2
x + -6 = -7.280109889 Simplifying x + -6 = -7.280109889 Reorder the terms: -6 + x = -7.280109889 Solving -6 + x = -7.280109889 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -7.280109889 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.280109889 + 6 x = -7.280109889 + 6 Combine like terms: -7.280109889 + 6 = -1.280109889 x = -1.280109889 Simplifying x = -1.280109889Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.280109889, -1.280109889}
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