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Simplifying 8x2 + 2x = 23 Reorder the terms: 2x + 8x2 = 23 Solving 2x + 8x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + 2x + 8x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + 2x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.875 + 0.25x + x2 = 0 Move the constant term to the right: Add '2.875' to each side of the equation. -2.875 + 0.25x + 2.875 + x2 = 0 + 2.875 Reorder the terms: -2.875 + 2.875 + 0.25x + x2 = 0 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + 0.25x + x2 = 0 + 2.875 0.25x + x2 = 0 + 2.875 Combine like terms: 0 + 2.875 = 2.875 0.25x + x2 = 2.875 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 = 2.875 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 2.875 + 0.015625 Combine like terms: 2.875 + 0.015625 = 2.890625 0.015625 + 0.25x + x2 = 2.890625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 2.890625 Calculate the square root of the right side: 1.700183814 Break this problem into two subproblems by setting (x + 0.125) equal to 1.700183814 and -1.700183814.Subproblem 1
x + 0.125 = 1.700183814 Simplifying x + 0.125 = 1.700183814 Reorder the terms: 0.125 + x = 1.700183814 Solving 0.125 + x = 1.700183814 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 = 1.700183814 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 1.700183814 + -0.125 x = 1.700183814 + -0.125 Combine like terms: 1.700183814 + -0.125 = 1.575183814 x = 1.575183814 Simplifying x = 1.575183814Subproblem 2
x + 0.125 = -1.700183814 Simplifying x + 0.125 = -1.700183814 Reorder the terms: 0.125 + x = -1.700183814 Solving 0.125 + x = -1.700183814 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 = -1.700183814 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -1.700183814 + -0.125 x = -1.700183814 + -0.125 Combine like terms: -1.700183814 + -0.125 = -1.825183814 x = -1.825183814 Simplifying x = -1.825183814Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.575183814, -1.825183814}
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