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Simplifying x2 + (0.000008) * x + -1(0.000000000004) = 0 Multiply -1 * 0.000000000004 x2 + 0.000008x + -0.000000000004 = 0 Reorder the terms: -0.000000000004 + 0.000008x + x2 = 0 Solving -0.000000000004 + 0.000008x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000000000004' to each side of the equation. -0.000000000004 + 0.000008x + 0.000000000004 + x2 = 0 + 0.000000000004 Reorder the terms: -0.000000000004 + 0.000000000004 + 0.000008x + x2 = 0 + 0.000000000004 Combine like terms: -0.000000000004 + 0.000000000004 = 0.000000000000 0.000000000000 + 0.000008x + x2 = 0 + 0.000000000004 0.000008x + x2 = 0 + 0.000000000004 Combine like terms: 0 + 0.000000000004 = 0.000000000004 0.000008x + x2 = 0.000000000004 The x term is 0.000008x. Take half its coefficient (0.000004). Square it (0.000000000016) and add it to both sides. Add '0.000000000016' to each side of the equation. 0.000008x + 0.000000000016 + x2 = 0.000000000004 + 0.000000000016 Reorder the terms: 0.000000000016 + 0.000008x + x2 = 0.000000000004 + 0.000000000016 Combine like terms: 0.000000000004 + 0.000000000016 = 0.00000000002 0.000000000016 + 0.000008x + x2 = 0.00000000002 Factor a perfect square on the left side: (x + 0.000004)(x + 0.000004) = 0.00000000002 Calculate the square root of the right side: 0.000004472 Break this problem into two subproblems by setting (x + 0.000004) equal to 0.000004472 and -0.000004472.Subproblem 1
x + 0.000004 = 0.000004472 Simplifying x + 0.000004 = 0.000004472 Reorder the terms: 0.000004 + x = 0.000004472 Solving 0.000004 + x = 0.000004472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000004' to each side of the equation. 0.000004 + -0.000004 + x = 0.000004472 + -0.000004 Combine like terms: 0.000004 + -0.000004 = 0.000000 0.000000 + x = 0.000004472 + -0.000004 x = 0.000004472 + -0.000004 Combine like terms: 0.000004472 + -0.000004 = 0.000000472 x = 0.000000472 Simplifying x = 0.000000472Subproblem 2
x + 0.000004 = -0.000004472 Simplifying x + 0.000004 = -0.000004472 Reorder the terms: 0.000004 + x = -0.000004472 Solving 0.000004 + x = -0.000004472 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.000004' to each side of the equation. 0.000004 + -0.000004 + x = -0.000004472 + -0.000004 Combine like terms: 0.000004 + -0.000004 = 0.000000 0.000000 + x = -0.000004472 + -0.000004 x = -0.000004472 + -0.000004 Combine like terms: -0.000004472 + -0.000004 = -0.000008472 x = -0.000008472 Simplifying x = -0.000008472Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000000472, -0.000008472}
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