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Simplifying 2x(4x + 1) = 7 Reorder the terms: 2x(1 + 4x) = 7 (1 * 2x + 4x * 2x) = 7 (2x + 8x2) = 7 Solving 2x + 8x2 = 7 Solving for variable 'x'. Reorder the terms: -7 + 2x + 8x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -7 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 0.25x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 0.25x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 0.25x + x2 = 0 + 0.875 0.25x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 0.25x + x2 = 0.875 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 = 0.875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.875 + 0.015625 Combine like terms: 0.875 + 0.015625 = 0.890625 0.015625 + 0.25x + x2 = 0.890625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.890625 Calculate the square root of the right side: 0.943729304 Break this problem into two subproblems by setting (x + 0.125) equal to 0.943729304 and -0.943729304.Subproblem 1
x + 0.125 = 0.943729304 Simplifying x + 0.125 = 0.943729304 Reorder the terms: 0.125 + x = 0.943729304 Solving 0.125 + x = 0.943729304 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 = 0.943729304 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.943729304 + -0.125 x = 0.943729304 + -0.125 Combine like terms: 0.943729304 + -0.125 = 0.818729304 x = 0.818729304 Simplifying x = 0.818729304Subproblem 2
x + 0.125 = -0.943729304 Simplifying x + 0.125 = -0.943729304 Reorder the terms: 0.125 + x = -0.943729304 Solving 0.125 + x = -0.943729304 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 = -0.943729304 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.943729304 + -0.125 x = -0.943729304 + -0.125 Combine like terms: -0.943729304 + -0.125 = -1.068729304 x = -1.068729304 Simplifying x = -1.068729304Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.818729304, -1.068729304}
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