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Simplifying x2 + -11x = -5x + 67 Reorder the terms: -11x + x2 = -5x + 67 Reorder the terms: -11x + x2 = 67 + -5x Solving -11x + x2 = 67 + -5x Solving for variable 'x'. Reorder the terms: -67 + -11x + 5x + x2 = 67 + -5x + -67 + 5x Combine like terms: -11x + 5x = -6x -67 + -6x + x2 = 67 + -5x + -67 + 5x Reorder the terms: -67 + -6x + x2 = 67 + -67 + -5x + 5x Combine like terms: 67 + -67 = 0 -67 + -6x + x2 = 0 + -5x + 5x -67 + -6x + x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -67 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '67' to each side of the equation. -67 + -6x + 67 + x2 = 0 + 67 Reorder the terms: -67 + 67 + -6x + x2 = 0 + 67 Combine like terms: -67 + 67 = 0 0 + -6x + x2 = 0 + 67 -6x + x2 = 0 + 67 Combine like terms: 0 + 67 = 67 -6x + x2 = 67 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 67 + 9 Reorder the terms: 9 + -6x + x2 = 67 + 9 Combine like terms: 67 + 9 = 76 9 + -6x + x2 = 76 Factor a perfect square on the left side: (x + -3)(x + -3) = 76 Calculate the square root of the right side: 8.717797887 Break this problem into two subproblems by setting (x + -3) equal to 8.717797887 and -8.717797887.Subproblem 1
x + -3 = 8.717797887 Simplifying x + -3 = 8.717797887 Reorder the terms: -3 + x = 8.717797887 Solving -3 + x = 8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 8.717797887 + 3 Combine like terms: -3 + 3 = 0 0 + x = 8.717797887 + 3 x = 8.717797887 + 3 Combine like terms: 8.717797887 + 3 = 11.717797887 x = 11.717797887 Simplifying x = 11.717797887Subproblem 2
x + -3 = -8.717797887 Simplifying x + -3 = -8.717797887 Reorder the terms: -3 + x = -8.717797887 Solving -3 + x = -8.717797887 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -8.717797887 + 3 Combine like terms: -3 + 3 = 0 0 + x = -8.717797887 + 3 x = -8.717797887 + 3 Combine like terms: -8.717797887 + 3 = -5.717797887 x = -5.717797887 Simplifying x = -5.717797887Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.717797887, -5.717797887}
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