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Simplifying x = -16x2 + 550 Reorder the terms: x = 550 + -16x2 Solving x = 550 + -16x2 Solving for variable 'x'. Reorder the terms: -550 + x + 16x2 = 550 + -16x2 + -550 + 16x2 Reorder the terms: -550 + x + 16x2 = 550 + -550 + -16x2 + 16x2 Combine like terms: 550 + -550 = 0 -550 + x + 16x2 = 0 + -16x2 + 16x2 -550 + x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -550 + x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -34.375 + 0.0625x + x2 = 0 Move the constant term to the right: Add '34.375' to each side of the equation. -34.375 + 0.0625x + 34.375 + x2 = 0 + 34.375 Reorder the terms: -34.375 + 34.375 + 0.0625x + x2 = 0 + 34.375 Combine like terms: -34.375 + 34.375 = 0.000 0.000 + 0.0625x + x2 = 0 + 34.375 0.0625x + x2 = 0 + 34.375 Combine like terms: 0 + 34.375 = 34.375 0.0625x + x2 = 34.375 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. 0.0625x + 0.25 + x2 = 34.375 + 0.25 Reorder the terms: 0.25 + 0.0625x + x2 = 34.375 + 0.25 Combine like terms: 34.375 + 0.25 = 34.625 0.25 + 0.0625x + x2 = 34.625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 34.625 Calculate the square root of the right side: 5.884301148 Break this problem into two subproblems by setting (x + 0.5) equal to 5.884301148 and -5.884301148.Subproblem 1
x + 0.5 = 5.884301148 Simplifying x + 0.5 = 5.884301148 Reorder the terms: 0.5 + x = 5.884301148 Solving 0.5 + x = 5.884301148 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 = 5.884301148 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.884301148 + -0.5 x = 5.884301148 + -0.5 Combine like terms: 5.884301148 + -0.5 = 5.384301148 x = 5.384301148 Simplifying x = 5.384301148Subproblem 2
x + 0.5 = -5.884301148 Simplifying x + 0.5 = -5.884301148 Reorder the terms: 0.5 + x = -5.884301148 Solving 0.5 + x = -5.884301148 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 = -5.884301148 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.884301148 + -0.5 x = -5.884301148 + -0.5 Combine like terms: -5.884301148 + -0.5 = -6.384301148 x = -6.384301148 Simplifying x = -6.384301148Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.384301148, -6.384301148}
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