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Simplifying x2 + 0.000013x + -0.0000026 = 0 Reorder the terms: -0.0000026 + 0.000013x + x2 = 0 Solving -0.0000026 + 0.000013x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.0000026' to each side of the equation. -0.0000026 + 0.000013x + 0.0000026 + x2 = 0 + 0.0000026 Reorder the terms: -0.0000026 + 0.0000026 + 0.000013x + x2 = 0 + 0.0000026 Combine like terms: -0.0000026 + 0.0000026 = 0.0000000 0.0000000 + 0.000013x + x2 = 0 + 0.0000026 0.000013x + x2 = 0 + 0.0000026 Combine like terms: 0 + 0.0000026 = 0.0000026 0.000013x + x2 = 0.0000026 The x term is 0.000013x. Take half its coefficient (0.0000065). Square it (0.00000000004225) and add it to both sides. Add '0.00000000004225' to each side of the equation. 0.000013x + 0.00000000004225 + x2 = 0.0000026 + 0.00000000004225 Reorder the terms: 0.00000000004225 + 0.000013x + x2 = 0.0000026 + 0.00000000004225 Combine like terms: 0.0000026 + 0.00000000004225 = 0.00000260004225 0.00000000004225 + 0.000013x + x2 = 0.00000260004225 Factor a perfect square on the left side: (x + 0.0000065)(x + 0.0000065) = 0.00000260004225 Calculate the square root of the right side: 0.001612465 Break this problem into two subproblems by setting (x + 0.0000065) equal to 0.001612465 and -0.001612465.Subproblem 1
x + 0.0000065 = 0.001612465 Simplifying x + 0.0000065 = 0.001612465 Reorder the terms: 0.0000065 + x = 0.001612465 Solving 0.0000065 + x = 0.001612465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000065' to each side of the equation. 0.0000065 + -0.0000065 + x = 0.001612465 + -0.0000065 Combine like terms: 0.0000065 + -0.0000065 = 0.0000000 0.0000000 + x = 0.001612465 + -0.0000065 x = 0.001612465 + -0.0000065 Combine like terms: 0.001612465 + -0.0000065 = 0.001605965 x = 0.001605965 Simplifying x = 0.001605965Subproblem 2
x + 0.0000065 = -0.001612465 Simplifying x + 0.0000065 = -0.001612465 Reorder the terms: 0.0000065 + x = -0.001612465 Solving 0.0000065 + x = -0.001612465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0000065' to each side of the equation. 0.0000065 + -0.0000065 + x = -0.001612465 + -0.0000065 Combine like terms: 0.0000065 + -0.0000065 = 0.0000000 0.0000000 + x = -0.001612465 + -0.0000065 x = -0.001612465 + -0.0000065 Combine like terms: -0.001612465 + -0.0000065 = -0.001618965 x = -0.001618965 Simplifying x = -0.001618965Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.001605965, -0.001618965}
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