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Simplifying x2 + -0.0016x + -0.0016 = 0 Reorder the terms: -0.0016 + -0.0016x + x2 = 0 Solving -0.0016 + -0.0016x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0016' to each side of the equation. -0.0016 + -0.0016x + 0.0016 + x2 = 0 + 0.0016 Reorder the terms: -0.0016 + 0.0016 + -0.0016x + x2 = 0 + 0.0016 Combine like terms: -0.0016 + 0.0016 = 0.0000 0.0000 + -0.0016x + x2 = 0 + 0.0016 -0.0016x + x2 = 0 + 0.0016 Combine like terms: 0 + 0.0016 = 0.0016 -0.0016x + x2 = 0.0016 The x term is -0.0016x. Take half its coefficient (-0.0008). Square it (0.00000064) and add it to both sides. Add '0.00000064' to each side of the equation. -0.0016x + 0.00000064 + x2 = 0.0016 + 0.00000064 Reorder the terms: 0.00000064 + -0.0016x + x2 = 0.0016 + 0.00000064 Combine like terms: 0.0016 + 0.00000064 = 0.00160064 0.00000064 + -0.0016x + x2 = 0.00160064 Factor a perfect square on the left side: (x + -0.0008)(x + -0.0008) = 0.00160064 Calculate the square root of the right side: 0.040007999 Break this problem into two subproblems by setting (x + -0.0008) equal to 0.040007999 and -0.040007999.Subproblem 1
x + -0.0008 = 0.040007999 Simplifying x + -0.0008 = 0.040007999 Reorder the terms: -0.0008 + x = 0.040007999 Solving -0.0008 + x = 0.040007999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0008' to each side of the equation. -0.0008 + 0.0008 + x = 0.040007999 + 0.0008 Combine like terms: -0.0008 + 0.0008 = 0.0000 0.0000 + x = 0.040007999 + 0.0008 x = 0.040007999 + 0.0008 Combine like terms: 0.040007999 + 0.0008 = 0.040807999 x = 0.040807999 Simplifying x = 0.040807999Subproblem 2
x + -0.0008 = -0.040007999 Simplifying x + -0.0008 = -0.040007999 Reorder the terms: -0.0008 + x = -0.040007999 Solving -0.0008 + x = -0.040007999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0008' to each side of the equation. -0.0008 + 0.0008 + x = -0.040007999 + 0.0008 Combine like terms: -0.0008 + 0.0008 = 0.0000 0.0000 + x = -0.040007999 + 0.0008 x = -0.040007999 + 0.0008 Combine like terms: -0.040007999 + 0.0008 = -0.039207999 x = -0.039207999 Simplifying x = -0.039207999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.040807999, -0.039207999}
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