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Simplifying 8(2 + x) * x = 5 Reorder the terms for easier multiplication: 8x(2 + x) = 5 (2 * 8x + x * 8x) = 5 (16x + 8x2) = 5 Solving 16x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + 16x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 16x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + 2x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + 2x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + 2x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + 2x + x2 = 0 + 0.625 2x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 2x + x2 = 0.625 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 = 0.625 + 1 Reorder the terms: 1 + 2x + x2 = 0.625 + 1 Combine like terms: 0.625 + 1 = 1.625 1 + 2x + x2 = 1.625 Factor a perfect square on the left side: (x + 1)(x + 1) = 1.625 Calculate the square root of the right side: 1.274754878 Break this problem into two subproblems by setting (x + 1) equal to 1.274754878 and -1.274754878.Subproblem 1
x + 1 = 1.274754878 Simplifying x + 1 = 1.274754878 Reorder the terms: 1 + x = 1.274754878 Solving 1 + x = 1.274754878 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 = 1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + x = 1.274754878 + -1 x = 1.274754878 + -1 Combine like terms: 1.274754878 + -1 = 0.274754878 x = 0.274754878 Simplifying x = 0.274754878Subproblem 2
x + 1 = -1.274754878 Simplifying x + 1 = -1.274754878 Reorder the terms: 1 + x = -1.274754878 Solving 1 + x = -1.274754878 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 = -1.274754878 + -1 Combine like terms: 1 + -1 = 0 0 + x = -1.274754878 + -1 x = -1.274754878 + -1 Combine like terms: -1.274754878 + -1 = -2.274754878 x = -2.274754878 Simplifying x = -2.274754878Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.274754878, -2.274754878}
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