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Simplifying x2 + 11x = 1959 Reorder the terms: 11x + x2 = 1959 Solving 11x + x2 = 1959 Solving for variable 'x'. Reorder the terms: -1959 + 11x + x2 = 1959 + -1959 Combine like terms: 1959 + -1959 = 0 -1959 + 11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1959' to each side of the equation. -1959 + 11x + 1959 + x2 = 0 + 1959 Reorder the terms: -1959 + 1959 + 11x + x2 = 0 + 1959 Combine like terms: -1959 + 1959 = 0 0 + 11x + x2 = 0 + 1959 11x + x2 = 0 + 1959 Combine like terms: 0 + 1959 = 1959 11x + x2 = 1959 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 = 1959 + 30.25 Reorder the terms: 30.25 + 11x + x2 = 1959 + 30.25 Combine like terms: 1959 + 30.25 = 1989.25 30.25 + 11x + x2 = 1989.25 Factor a perfect square on the left side: (x + 5.5)(x + 5.5) = 1989.25 Calculate the square root of the right side: 44.601008957 Break this problem into two subproblems by setting (x + 5.5) equal to 44.601008957 and -44.601008957.Subproblem 1
x + 5.5 = 44.601008957 Simplifying x + 5.5 = 44.601008957 Reorder the terms: 5.5 + x = 44.601008957 Solving 5.5 + x = 44.601008957 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 = 44.601008957 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = 44.601008957 + -5.5 x = 44.601008957 + -5.5 Combine like terms: 44.601008957 + -5.5 = 39.101008957 x = 39.101008957 Simplifying x = 39.101008957Subproblem 2
x + 5.5 = -44.601008957 Simplifying x + 5.5 = -44.601008957 Reorder the terms: 5.5 + x = -44.601008957 Solving 5.5 + x = -44.601008957 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 = -44.601008957 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + x = -44.601008957 + -5.5 x = -44.601008957 + -5.5 Combine like terms: -44.601008957 + -5.5 = -50.101008957 x = -50.101008957 Simplifying x = -50.101008957Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.101008957, -50.101008957}
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