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Simplifying x2 + -0.017x + -0.064 = 0 Reorder the terms: -0.064 + -0.017x + x2 = 0 Solving -0.064 + -0.017x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.064' to each side of the equation. -0.064 + -0.017x + 0.064 + x2 = 0 + 0.064 Reorder the terms: -0.064 + 0.064 + -0.017x + x2 = 0 + 0.064 Combine like terms: -0.064 + 0.064 = 0.000 0.000 + -0.017x + x2 = 0 + 0.064 -0.017x + x2 = 0 + 0.064 Combine like terms: 0 + 0.064 = 0.064 -0.017x + x2 = 0.064 The x term is -0.017x. Take half its coefficient (-0.0085). Square it (0.00007225) and add it to both sides. Add '0.00007225' to each side of the equation. -0.017x + 0.00007225 + x2 = 0.064 + 0.00007225 Reorder the terms: 0.00007225 + -0.017x + x2 = 0.064 + 0.00007225 Combine like terms: 0.064 + 0.00007225 = 0.06407225 0.00007225 + -0.017x + x2 = 0.06407225 Factor a perfect square on the left side: (x + -0.0085)(x + -0.0085) = 0.06407225 Calculate the square root of the right side: 0.253124969 Break this problem into two subproblems by setting (x + -0.0085) equal to 0.253124969 and -0.253124969.Subproblem 1
x + -0.0085 = 0.253124969 Simplifying x + -0.0085 = 0.253124969 Reorder the terms: -0.0085 + x = 0.253124969 Solving -0.0085 + x = 0.253124969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0085' to each side of the equation. -0.0085 + 0.0085 + x = 0.253124969 + 0.0085 Combine like terms: -0.0085 + 0.0085 = 0.0000 0.0000 + x = 0.253124969 + 0.0085 x = 0.253124969 + 0.0085 Combine like terms: 0.253124969 + 0.0085 = 0.261624969 x = 0.261624969 Simplifying x = 0.261624969Subproblem 2
x + -0.0085 = -0.253124969 Simplifying x + -0.0085 = -0.253124969 Reorder the terms: -0.0085 + x = -0.253124969 Solving -0.0085 + x = -0.253124969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0085' to each side of the equation. -0.0085 + 0.0085 + x = -0.253124969 + 0.0085 Combine like terms: -0.0085 + 0.0085 = 0.0000 0.0000 + x = -0.253124969 + 0.0085 x = -0.253124969 + 0.0085 Combine like terms: -0.253124969 + 0.0085 = -0.244624969 x = -0.244624969 Simplifying x = -0.244624969Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.261624969, -0.244624969}
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