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Simplifying x2 + -89x = 9 Reorder the terms: -89x + x2 = 9 Solving -89x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -89x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -89x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -89x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -89x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -89x + x2 = 0 + 9 -89x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -89x + x2 = 9 The x term is -89x. Take half its coefficient (-44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. -89x + 1980.25 + x2 = 9 + 1980.25 Reorder the terms: 1980.25 + -89x + x2 = 9 + 1980.25 Combine like terms: 9 + 1980.25 = 1989.25 1980.25 + -89x + x2 = 1989.25 Factor a perfect square on the left side: (x + -44.5)(x + -44.5) = 1989.25 Calculate the square root of the right side: 44.601008957 Break this problem into two subproblems by setting (x + -44.5) equal to 44.601008957 and -44.601008957.Subproblem 1
x + -44.5 = 44.601008957 Simplifying x + -44.5 = 44.601008957 Reorder the terms: -44.5 + x = 44.601008957 Solving -44.5 + x = 44.601008957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = 44.601008957 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = 44.601008957 + 44.5 x = 44.601008957 + 44.5 Combine like terms: 44.601008957 + 44.5 = 89.101008957 x = 89.101008957 Simplifying x = 89.101008957Subproblem 2
x + -44.5 = -44.601008957 Simplifying x + -44.5 = -44.601008957 Reorder the terms: -44.5 + x = -44.601008957 Solving -44.5 + x = -44.601008957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = -44.601008957 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = -44.601008957 + 44.5 x = -44.601008957 + 44.5 Combine like terms: -44.601008957 + 44.5 = -0.101008957 x = -0.101008957 Simplifying x = -0.101008957Solution
The solution to the problem is based on the solutions from the subproblems. x = {89.101008957, -0.101008957}
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