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Simplifying (x * x) + 0.00008x + -0.000000002 = 0 Multiply x * x (x2) + 0.00008x + -0.000000002 = 0 x2 + 0.00008x + -0.000000002 = 0 Reorder the terms: -0.000000002 + 0.00008x + x2 = 0 Solving -0.000000002 + 0.00008x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.000000002' to each side of the equation. -0.000000002 + 0.00008x + 0.000000002 + x2 = 0 + 0.000000002 Reorder the terms: -0.000000002 + 0.000000002 + 0.00008x + x2 = 0 + 0.000000002 Combine like terms: -0.000000002 + 0.000000002 = 0.000000000 0.000000000 + 0.00008x + x2 = 0 + 0.000000002 0.00008x + x2 = 0 + 0.000000002 Combine like terms: 0 + 0.000000002 = 0.000000002 0.00008x + x2 = 0.000000002 The x term is 0.00008x. Take half its coefficient (0.00004). Square it (0.0000000016) and add it to both sides. Add '0.0000000016' to each side of the equation. 0.00008x + 0.0000000016 + x2 = 0.000000002 + 0.0000000016 Reorder the terms: 0.0000000016 + 0.00008x + x2 = 0.000000002 + 0.0000000016 Combine like terms: 0.000000002 + 0.0000000016 = 0.0000000036 0.0000000016 + 0.00008x + x2 = 0.0000000036 Factor a perfect square on the left side: (x + 0.00004)(x + 0.00004) = 0.0000000036 Calculate the square root of the right side: 0.00006 Break this problem into two subproblems by setting (x + 0.00004) equal to 0.00006 and -0.00006.Subproblem 1
x + 0.00004 = 0.00006 Simplifying x + 0.00004 = 0.00006 Reorder the terms: 0.00004 + x = 0.00006 Solving 0.00004 + x = 0.00006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00004' to each side of the equation. 0.00004 + -0.00004 + x = 0.00006 + -0.00004 Combine like terms: 0.00004 + -0.00004 = 0.00000 0.00000 + x = 0.00006 + -0.00004 x = 0.00006 + -0.00004 Combine like terms: 0.00006 + -0.00004 = 0.00002 x = 0.00002 Simplifying x = 0.00002Subproblem 2
x + 0.00004 = -0.00006 Simplifying x + 0.00004 = -0.00006 Reorder the terms: 0.00004 + x = -0.00006 Solving 0.00004 + x = -0.00006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00004' to each side of the equation. 0.00004 + -0.00004 + x = -0.00006 + -0.00004 Combine like terms: 0.00004 + -0.00004 = 0.00000 0.00000 + x = -0.00006 + -0.00004 x = -0.00006 + -0.00004 Combine like terms: -0.00006 + -0.00004 = -0.0001 x = -0.0001 Simplifying x = -0.0001Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.00002, -0.0001}
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