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Simplifying 8(2 + x) * x = 0.5 Reorder the terms for easier multiplication: 8x(2 + x) = 0.5 (2 * 8x + x * 8x) = 0.5 (16x + 8x2) = 0.5 Solving 16x + 8x2 = 0.5 Solving for variable 'x'. Reorder the terms: -0.5 + 16x + 8x2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -0.5 + 16x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.0625 + 2x + x2 = 0.0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + 2x + 0.0625 + x2 = 0.0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + 2x + x2 = 0.0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + 2x + x2 = 0.0 + 0.0625 2x + x2 = 0.0 + 0.0625 Combine like terms: 0.0 + 0.0625 = 0.0625 2x + x2 = 0.0625 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 0.0625 + 1 Reorder the terms: 1 + 2x + x2 = 0.0625 + 1 Combine like terms: 0.0625 + 1 = 1.0625 1 + 2x + x2 = 1.0625 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (x + 1) equal to 1.030776406 and -1.030776406.Subproblem 1
x + 1 = 1.030776406 Simplifying x + 1 = 1.030776406 Reorder the terms: 1 + x = 1.030776406 Solving 1 + x = 1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 1.030776406 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.030776406 + -1 x = 1.030776406 + -1 Combine like terms: 1.030776406 + -1 = 0.030776406 x = 0.030776406 Simplifying x = 0.030776406Subproblem 2
x + 1 = -1.030776406 Simplifying x + 1 = -1.030776406 Reorder the terms: 1 + x = -1.030776406 Solving 1 + x = -1.030776406 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -1.030776406 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.030776406 + -1 x = -1.030776406 + -1 Combine like terms: -1.030776406 + -1 = -2.030776406 x = -2.030776406 Simplifying x = -2.030776406Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.030776406, -2.030776406}
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