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Simplifying 2x(4x + 1) = 5 Reorder the terms: 2x(1 + 4x) = 5 (1 * 2x + 4x * 2x) = 5 (2x + 8x2) = 5 Solving 2x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 2x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 0.25x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 0.25x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 0.25x + x2 = 0 + 0.625 0.25x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 0.25x + x2 = 0.625 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 = 0.625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.625 + 0.015625 Combine like terms: 0.625 + 0.015625 = 0.640625 0.015625 + 0.25x + x2 = 0.640625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.640625 Calculate the square root of the right side: 0.80039053 Break this problem into two subproblems by setting (x + 0.125) equal to 0.80039053 and -0.80039053.Subproblem 1
x + 0.125 = 0.80039053 Simplifying x + 0.125 = 0.80039053 Reorder the terms: 0.125 + x = 0.80039053 Solving 0.125 + x = 0.80039053 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 = 0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.80039053 + -0.125 x = 0.80039053 + -0.125 Combine like terms: 0.80039053 + -0.125 = 0.67539053 x = 0.67539053 Simplifying x = 0.67539053Subproblem 2
x + 0.125 = -0.80039053 Simplifying x + 0.125 = -0.80039053 Reorder the terms: 0.125 + x = -0.80039053 Solving 0.125 + x = -0.80039053 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 = -0.80039053 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.80039053 + -0.125 x = -0.80039053 + -0.125 Combine like terms: -0.80039053 + -0.125 = -0.92539053 x = -0.92539053 Simplifying x = -0.92539053Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67539053, -0.92539053}
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