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Simplifying 4x2 = 0.000232 + -0.00464x Solving 4x2 = 0.000232 + -0.00464x Solving for variable 'x'. Reorder the terms: -0.000232 + 0.00464x + 4x2 = 0.000232 + -0.00464x + -0.000232 + 0.00464x Reorder the terms: -0.000232 + 0.00464x + 4x2 = 0.000232 + -0.000232 + -0.00464x + 0.00464x Combine like terms: 0.000232 + -0.000232 = 0.000000 -0.000232 + 0.00464x + 4x2 = 0.000000 + -0.00464x + 0.00464x -0.000232 + 0.00464x + 4x2 = -0.00464x + 0.00464x Combine like terms: -0.00464x + 0.00464x = 0.00000 -0.000232 + 0.00464x + 4x2 = 0.00000 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.000058 + 0.00116x + x2 = 0.00000 Move the constant term to the right: Add '0.000058' to each side of the equation. -0.000058 + 0.00116x + 0.000058 + x2 = 0.00000 + 0.000058 Reorder the terms: -0.000058 + 0.000058 + 0.00116x + x2 = 0.00000 + 0.000058 Combine like terms: -0.000058 + 0.000058 = 0.000000 0.000000 + 0.00116x + x2 = 0.00000 + 0.000058 0.00116x + x2 = 0.00000 + 0.000058 Combine like terms: 0.00000 + 0.000058 = 0.000058 0.00116x + x2 = 0.000058 The x term is 0.00116x. Take half its coefficient (0.00058). Square it (0.0000003364) and add it to both sides. Add '0.0000003364' to each side of the equation. 0.00116x + 0.0000003364 + x2 = 0.000058 + 0.0000003364 Reorder the terms: 0.0000003364 + 0.00116x + x2 = 0.000058 + 0.0000003364 Combine like terms: 0.000058 + 0.0000003364 = 0.0000583364 0.0000003364 + 0.00116x + x2 = 0.0000583364 Factor a perfect square on the left side: (x + 0.00058)(x + 0.00058) = 0.0000583364 Calculate the square root of the right side: 0.007637827 Break this problem into two subproblems by setting (x + 0.00058) equal to 0.007637827 and -0.007637827.Subproblem 1
x + 0.00058 = 0.007637827 Simplifying x + 0.00058 = 0.007637827 Reorder the terms: 0.00058 + x = 0.007637827 Solving 0.00058 + x = 0.007637827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00058' to each side of the equation. 0.00058 + -0.00058 + x = 0.007637827 + -0.00058 Combine like terms: 0.00058 + -0.00058 = 0.00000 0.00000 + x = 0.007637827 + -0.00058 x = 0.007637827 + -0.00058 Combine like terms: 0.007637827 + -0.00058 = 0.007057827 x = 0.007057827 Simplifying x = 0.007057827Subproblem 2
x + 0.00058 = -0.007637827 Simplifying x + 0.00058 = -0.007637827 Reorder the terms: 0.00058 + x = -0.007637827 Solving 0.00058 + x = -0.007637827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.00058' to each side of the equation. 0.00058 + -0.00058 + x = -0.007637827 + -0.00058 Combine like terms: 0.00058 + -0.00058 = 0.00000 0.00000 + x = -0.007637827 + -0.00058 x = -0.007637827 + -0.00058 Combine like terms: -0.007637827 + -0.00058 = -0.008217827 x = -0.008217827 Simplifying x = -0.008217827Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.007057827, -0.008217827}
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