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Simplifying 16x2 + -1 = x Reorder the terms: -1 + 16x2 = x Solving -1 + 16x2 = x Solving for variable 'x'. Reorder the terms: -1 + -1x + 16x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -1x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + -0.0625x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.0625x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.0625x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.0625x + x2 = 0 + 0.0625 -0.0625x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.0625x + x2 = 0.0625 The x term is -0.0625x. Take half its coefficient (-0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. -0.0625x + 0.0009765625 + x2 = 0.0625 + 0.0009765625 Reorder the terms: 0.0009765625 + -0.0625x + x2 = 0.0625 + 0.0009765625 Combine like terms: 0.0625 + 0.0009765625 = 0.0634765625 0.0009765625 + -0.0625x + x2 = 0.0634765625 Factor a perfect square on the left side: (x + -0.03125)(x + -0.03125) = 0.0634765625 Calculate the square root of the right side: 0.251945555 Break this problem into two subproblems by setting (x + -0.03125) equal to 0.251945555 and -0.251945555.Subproblem 1
x + -0.03125 = 0.251945555 Simplifying x + -0.03125 = 0.251945555 Reorder the terms: -0.03125 + x = 0.251945555 Solving -0.03125 + x = 0.251945555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = 0.251945555 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = 0.251945555 + 0.03125 x = 0.251945555 + 0.03125 Combine like terms: 0.251945555 + 0.03125 = 0.283195555 x = 0.283195555 Simplifying x = 0.283195555Subproblem 2
x + -0.03125 = -0.251945555 Simplifying x + -0.03125 = -0.251945555 Reorder the terms: -0.03125 + x = -0.251945555 Solving -0.03125 + x = -0.251945555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03125' to each side of the equation. -0.03125 + 0.03125 + x = -0.251945555 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + x = -0.251945555 + 0.03125 x = -0.251945555 + 0.03125 Combine like terms: -0.251945555 + 0.03125 = -0.220695555 x = -0.220695555 Simplifying x = -0.220695555Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.283195555, -0.220695555}
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