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Simplifying 862.068965517x2 + x + -0.05 = 0 Reorder the terms: -0.05 + x + 862.068965517x2 = 0 Solving -0.05 + x + 862.068965517x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 862.068965517 the coefficient of the squared term: Divide each side by '862.068965517'. -0.000058 + 0.001160000000x + x2 = 0 Move the constant term to the right: Add '0.000058' to each side of the equation. -0.000058 + 0.001160000000x + 0.000058 + x2 = 0 + 0.000058 Reorder the terms: -0.000058 + 0.000058 + 0.001160000000x + x2 = 0 + 0.000058 Combine like terms: -0.000058 + 0.000058 = 0.000000 0.000000 + 0.001160000000x + x2 = 0 + 0.000058 0.001160000000x + x2 = 0 + 0.000058 Combine like terms: 0 + 0.000058 = 0.000058 0.001160000000x + x2 = 0.000058 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. 0.001160000000x + 0.25 + x2 = 0.000058 + 0.25 Reorder the terms: 0.25 + 0.001160000000x + x2 = 0.000058 + 0.25 Combine like terms: 0.000058 + 0.25 = 0.250058 0.25 + 0.001160000000x + x2 = 0.250058 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.250058 Calculate the square root of the right side: 0.500057997 Break this problem into two subproblems by setting (x + 0.5) equal to 0.500057997 and -0.500057997.Subproblem 1
x + 0.5 = 0.500057997 Simplifying x + 0.5 = 0.500057997 Reorder the terms: 0.5 + x = 0.500057997 Solving 0.5 + x = 0.500057997 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 = 0.500057997 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.500057997 + -0.5 x = 0.500057997 + -0.5 Combine like terms: 0.500057997 + -0.5 = 0.000057997 x = 0.000057997 Simplifying x = 0.000057997Subproblem 2
x + 0.5 = -0.500057997 Simplifying x + 0.5 = -0.500057997 Reorder the terms: 0.5 + x = -0.500057997 Solving 0.5 + x = -0.500057997 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 = -0.500057997 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.500057997 + -0.5 x = -0.500057997 + -0.5 Combine like terms: -0.500057997 + -0.5 = -1.000057997 x = -1.000057997 Simplifying x = -1.000057997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000057997, -1.000057997}
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