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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 = 1.054247642 x = 1.054247642 Simplifying x = 1.054247642Subproblem 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 = -1.304247642 x = -1.304247642 Simplifying x = -1.304247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.054247642, -1.304247642}
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