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Simplifying x + 4x2 = 0.0000041 Solving x + 4x2 = 0.0000041 Solving for variable 'x'. Reorder the terms: -0.0000041 + x + 4x2 = 0.0000041 + -0.0000041 Combine like terms: 0.0000041 + -0.0000041 = 0.0000000 -0.0000041 + x + 4x2 = 0.0000000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.000001025 + 0.25x + x2 = 0.0000000 Move the constant term to the right: Add '0.000001025' to each side of the equation. -0.000001025 + 0.25x + 0.000001025 + x2 = 0.0000000 + 0.000001025 Reorder the terms: -0.000001025 + 0.000001025 + 0.25x + x2 = 0.0000000 + 0.000001025 Combine like terms: -0.000001025 + 0.000001025 = 0.000000000 0.000000000 + 0.25x + x2 = 0.0000000 + 0.000001025 0.25x + x2 = 0.0000000 + 0.000001025 Combine like terms: 0.0000000 + 0.000001025 = 0.000001025 0.25x + x2 = 0.000001025 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.25x + 0.25 + x2 = 0.000001025 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 0.000001025 + 0.25 Combine like terms: 0.000001025 + 0.25 = 0.250001025 0.25 + 0.25x + x2 = 0.250001025 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.250001025 Calculate the square root of the right side: 0.500001025 Break this problem into two subproblems by setting (x + 0.5) equal to 0.500001025 and -0.500001025.Subproblem 1
x + 0.5 = 0.500001025 Simplifying x + 0.5 = 0.500001025 Reorder the terms: 0.5 + x = 0.500001025 Solving 0.5 + x = 0.500001025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.500001025 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500001025 + -0.5 x = 0.500001025 + -0.5 Combine like terms: 0.500001025 + -0.5 = 0.000001025 x = 0.000001025 Simplifying x = 0.000001025Subproblem 2
x + 0.5 = -0.500001025 Simplifying x + 0.5 = -0.500001025 Reorder the terms: 0.5 + x = -0.500001025 Solving 0.5 + x = -0.500001025 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.500001025 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500001025 + -0.5 x = -0.500001025 + -0.5 Combine like terms: -0.500001025 + -0.5 = -1.000001025 x = -1.000001025 Simplifying x = -1.000001025Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000001025, -1.000001025}
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