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Simplifying 16x2 + 4x + -1 = 0 Reorder the terms: -1 + 4x + 16x2 = 0 Solving -1 + 4x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.0625 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 0.25x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 0.25x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 0.25x + x2 = 0 + 0.0625 0.25x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 0.25x + x2 = 0.0625 The x term is 0.25x. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25x + 0.015625 + x2 = 0.0625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.0625 + 0.015625 Combine like terms: 0.0625 + 0.015625 = 0.078125 0.015625 + 0.25x + x2 = 0.078125 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.078125 Calculate the square root of the right side: 0.279508497 Break this problem into two subproblems by setting (x + 0.125) equal to 0.279508497 and -0.279508497.Subproblem 1
x + 0.125 = 0.279508497 Simplifying x + 0.125 = 0.279508497 Reorder the terms: 0.125 + x = 0.279508497 Solving 0.125 + x = 0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = 0.279508497 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.279508497 + -0.125 x = 0.279508497 + -0.125 Combine like terms: 0.279508497 + -0.125 = 0.154508497 x = 0.154508497 Simplifying x = 0.154508497Subproblem 2
x + 0.125 = -0.279508497 Simplifying x + 0.125 = -0.279508497 Reorder the terms: 0.125 + x = -0.279508497 Solving 0.125 + x = -0.279508497 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + x = -0.279508497 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.279508497 + -0.125 x = -0.279508497 + -0.125 Combine like terms: -0.279508497 + -0.125 = -0.404508497 x = -0.404508497 Simplifying x = -0.404508497Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.154508497, -0.404508497}
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