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Simplifying 0.002 + -0.00138x + -3.99977x2 = 0 Solving 0.002 + -0.00138x + -3.99977x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3.99977 the coefficient of the squared term: Divide each side by '-3.99977'. -0.0005000287517 + 0.0003450198386x + x2 = 0 Move the constant term to the right: Add '0.0005000287517' to each side of the equation. -0.0005000287517 + 0.0003450198386x + 0.0005000287517 + x2 = 0 + 0.0005000287517 Reorder the terms: -0.0005000287517 + 0.0005000287517 + 0.0003450198386x + x2 = 0 + 0.0005000287517 Combine like terms: -0.0005000287517 + 0.0005000287517 = 0.0000000000000 0.0000000000000 + 0.0003450198386x + x2 = 0 + 0.0005000287517 0.0003450198386x + x2 = 0 + 0.0005000287517 Combine like terms: 0 + 0.0005000287517 = 0.0005000287517 0.0003450198386x + x2 = 0.0005000287517 The x term is 0.0003450198386x. Take half its coefficient (0.0001725099193). Square it (0.00000002975967226) and add it to both sides. Add '0.00000002975967226' to each side of the equation. 0.0003450198386x + 0.00000002975967226 + x2 = 0.0005000287517 + 0.00000002975967226 Reorder the terms: 0.00000002975967226 + 0.0003450198386x + x2 = 0.0005000287517 + 0.00000002975967226 Combine like terms: 0.0005000287517 + 0.00000002975967226 = 0.00050005851137226 0.00000002975967226 + 0.0003450198386x + x2 = 0.00050005851137226 Factor a perfect square on the left side: (x + 0.0001725099193)(x + 0.0001725099193) = 0.00050005851137226 Calculate the square root of the right side: 0.022361988 Break this problem into two subproblems by setting (x + 0.0001725099193) equal to 0.022361988 and -0.022361988.Subproblem 1
x + 0.0001725099193 = 0.022361988 Simplifying x + 0.0001725099193 = 0.022361988 Reorder the terms: 0.0001725099193 + x = 0.022361988 Solving 0.0001725099193 + x = 0.022361988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001725099193' to each side of the equation. 0.0001725099193 + -0.0001725099193 + x = 0.022361988 + -0.0001725099193 Combine like terms: 0.0001725099193 + -0.0001725099193 = 0.0000000000000 0.0000000000000 + x = 0.022361988 + -0.0001725099193 x = 0.022361988 + -0.0001725099193 Combine like terms: 0.022361988 + -0.0001725099193 = 0.0221894780807 x = 0.0221894780807 Simplifying x = 0.0221894780807Subproblem 2
x + 0.0001725099193 = -0.022361988 Simplifying x + 0.0001725099193 = -0.022361988 Reorder the terms: 0.0001725099193 + x = -0.022361988 Solving 0.0001725099193 + x = -0.022361988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0001725099193' to each side of the equation. 0.0001725099193 + -0.0001725099193 + x = -0.022361988 + -0.0001725099193 Combine like terms: 0.0001725099193 + -0.0001725099193 = 0.0000000000000 0.0000000000000 + x = -0.022361988 + -0.0001725099193 x = -0.022361988 + -0.0001725099193 Combine like terms: -0.022361988 + -0.0001725099193 = -0.0225344979193 x = -0.0225344979193 Simplifying x = -0.0225344979193Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0221894780807, -0.0225344979193}
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