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Simplifying x2 + -61.28x = 2000 Reorder the terms: -61.28x + x2 = 2000 Solving -61.28x + x2 = 2000 Solving for variable 'x'. Reorder the terms: -2000 + -61.28x + x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + -61.28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2000' to each side of the equation. -2000 + -61.28x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + -61.28x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + -61.28x + x2 = 0 + 2000 -61.28x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 -61.28x + x2 = 2000 The x term is -61.28x. Take half its coefficient (-30.64). Square it (938.8096) and add it to both sides. Add '938.8096' to each side of the equation. -61.28x + 938.8096 + x2 = 2000 + 938.8096 Reorder the terms: 938.8096 + -61.28x + x2 = 2000 + 938.8096 Combine like terms: 2000 + 938.8096 = 2938.8096 938.8096 + -61.28x + x2 = 2938.8096 Factor a perfect square on the left side: (x + -30.64)(x + -30.64) = 2938.8096 Calculate the square root of the right side: 54.210788594 Break this problem into two subproblems by setting (x + -30.64) equal to 54.210788594 and -54.210788594.Subproblem 1
x + -30.64 = 54.210788594 Simplifying x + -30.64 = 54.210788594 Reorder the terms: -30.64 + x = 54.210788594 Solving -30.64 + x = 54.210788594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.64' to each side of the equation. -30.64 + 30.64 + x = 54.210788594 + 30.64 Combine like terms: -30.64 + 30.64 = 0.00 0.00 + x = 54.210788594 + 30.64 x = 54.210788594 + 30.64 Combine like terms: 54.210788594 + 30.64 = 84.850788594 x = 84.850788594 Simplifying x = 84.850788594Subproblem 2
x + -30.64 = -54.210788594 Simplifying x + -30.64 = -54.210788594 Reorder the terms: -30.64 + x = -54.210788594 Solving -30.64 + x = -54.210788594 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30.64' to each side of the equation. -30.64 + 30.64 + x = -54.210788594 + 30.64 Combine like terms: -30.64 + 30.64 = 0.00 0.00 + x = -54.210788594 + 30.64 x = -54.210788594 + 30.64 Combine like terms: -54.210788594 + 30.64 = -23.570788594 x = -23.570788594 Simplifying x = -23.570788594Solution
The solution to the problem is based on the solutions from the subproblems. x = {84.850788594, -23.570788594}
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