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Simplifying 16x2 + x = 316 Reorder the terms: x + 16x2 = 316 Solving x + 16x2 = 316 Solving for variable 'x'. Reorder the terms: -316 + x + 16x2 = 316 + -316 Combine like terms: 316 + -316 = 0 -316 + x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -19.75 + 0.0625x + x2 = 0 Move the constant term to the right: Add '19.75' to each side of the equation. -19.75 + 0.0625x + 19.75 + x2 = 0 + 19.75 Reorder the terms: -19.75 + 19.75 + 0.0625x + x2 = 0 + 19.75 Combine like terms: -19.75 + 19.75 = 0.00 0.00 + 0.0625x + x2 = 0 + 19.75 0.0625x + x2 = 0 + 19.75 Combine like terms: 0 + 19.75 = 19.75 0.0625x + x2 = 19.75 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 = 19.75 + 0.25 Reorder the terms: 0.25 + 0.0625x + x2 = 19.75 + 0.25 Combine like terms: 19.75 + 0.25 = 20 0.25 + 0.0625x + x2 = 20 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + 0.5) equal to 4.472135955 and -4.472135955.Subproblem 1
x + 0.5 = 4.472135955 Simplifying x + 0.5 = 4.472135955 Reorder the terms: 0.5 + x = 4.472135955 Solving 0.5 + x = 4.472135955 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 = 4.472135955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.472135955 + -0.5 x = 4.472135955 + -0.5 Combine like terms: 4.472135955 + -0.5 = 3.972135955 x = 3.972135955 Simplifying x = 3.972135955Subproblem 2
x + 0.5 = -4.472135955 Simplifying x + 0.5 = -4.472135955 Reorder the terms: 0.5 + x = -4.472135955 Solving 0.5 + x = -4.472135955 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 = -4.472135955 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.472135955 + -0.5 x = -4.472135955 + -0.5 Combine like terms: -4.472135955 + -0.5 = -4.972135955 x = -4.972135955 Simplifying x = -4.972135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.972135955, -4.972135955}
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