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Simplifying 2x(4x + -1) = 11 Reorder the terms: 2x(-1 + 4x) = 11 (-1 * 2x + 4x * 2x) = 11 (-2x + 8x2) = 11 Solving -2x + 8x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + -2x + 8x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + -2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.375 + -0.25x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + -0.25x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + -0.25x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + -0.25x + x2 = 0 + 1.375 -0.25x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 -0.25x + x2 = 1.375 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 = 1.375 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 1.375 + 0.015625 Combine like terms: 1.375 + 0.015625 = 1.390625 0.015625 + -0.25x + x2 = 1.390625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -0.125) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -0.125 = 1.179247642 Simplifying x + -0.125 = 1.179247642 Reorder the terms: -0.125 + x = 1.179247642 Solving -0.125 + x = 1.179247642 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 = 1.179247642 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 1.179247642 + 0.125 x = 1.179247642 + 0.125 Combine like terms: 1.179247642 + 0.125 = 1.304247642 x = 1.304247642 Simplifying x = 1.304247642Subproblem 2
x + -0.125 = -1.179247642 Simplifying x + -0.125 = -1.179247642 Reorder the terms: -0.125 + x = -1.179247642 Solving -0.125 + x = -1.179247642 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 = -1.179247642 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -1.179247642 + 0.125 x = -1.179247642 + 0.125 Combine like terms: -1.179247642 + 0.125 = -1.054247642 x = -1.054247642 Simplifying x = -1.054247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.304247642, -1.054247642}
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