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Simplifying x = x2 + 12x + -45 Reorder the terms: x = -45 + 12x + x2 Solving x = -45 + 12x + x2 Solving for variable 'x'. Reorder the terms: 45 + x + -12x + -1x2 = -45 + 12x + x2 + 45 + -12x + -1x2 Combine like terms: x + -12x = -11x 45 + -11x + -1x2 = -45 + 12x + x2 + 45 + -12x + -1x2 Reorder the terms: 45 + -11x + -1x2 = -45 + 45 + 12x + -12x + x2 + -1x2 Combine like terms: -45 + 45 = 0 45 + -11x + -1x2 = 0 + 12x + -12x + x2 + -1x2 45 + -11x + -1x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 45 + -11x + -1x2 = 0 + x2 + -1x2 45 + -11x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 45 + -11x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -45 + 11x + x2 = 0 Move the constant term to the right: Add '45' to each side of the equation. -45 + 11x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 11x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 11x + x2 = 0 + 45 11x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 11x + x2 = 45 The x term is 11x. Take half its coefficient (5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. 11x + 30.25 + x2 = 45 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 45 + 30.25 Combine like terms: 45 + 30.25 = 75.25 30.25 + 11x + x2 = 75.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 75.25 Calculate the square root of the right side: 8.674675786 Break this problem into two subproblems by setting (x + 5.5) equal to 8.674675786 and -8.674675786.Subproblem 1
x + 5.5 = 8.674675786 Simplifying x + 5.5 = 8.674675786 Reorder the terms: 5.5 + x = 8.674675786 Solving 5.5 + x = 8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = 8.674675786 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 8.674675786 + -5.5 x = 8.674675786 + -5.5 Combine like terms: 8.674675786 + -5.5 = 3.174675786 x = 3.174675786 Simplifying x = 3.174675786Subproblem 2
x + 5.5 = -8.674675786 Simplifying x + 5.5 = -8.674675786 Reorder the terms: 5.5 + x = -8.674675786 Solving 5.5 + x = -8.674675786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.5' to each side of the equation. 5.5 + -5.5 + x = -8.674675786 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -8.674675786 + -5.5 x = -8.674675786 + -5.5 Combine like terms: -8.674675786 + -5.5 = -14.174675786 x = -14.174675786 Simplifying x = -14.174675786Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.174675786, -14.174675786}
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