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Simplifying x + 8x * x = 2.5 Multiply x * x x + 8x2 = 2.5 Solving x + 8x2 = 2.5 Solving for variable 'x'. Reorder the terms: -2.5 + x + 8x2 = 2.5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + x + 8x2 = 0.0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.3125 + 0.125x + x2 = 0.0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + 0.125x + 0.3125 + x2 = 0.0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + 0.125x + x2 = 0.0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + 0.125x + x2 = 0.0 + 0.3125 0.125x + x2 = 0.0 + 0.3125 Combine like terms: 0.0 + 0.3125 = 0.3125 0.125x + x2 = 0.3125 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125x + 0.25 + x2 = 0.3125 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 0.3125 + 0.25 Combine like terms: 0.3125 + 0.25 = 0.5625 0.25 + 0.125x + x2 = 0.5625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.5625 Calculate the square root of the right side: 0.75 Break this problem into two subproblems by setting (x + 0.5) equal to 0.75 and -0.75.Subproblem 1
x + 0.5 = 0.75 Simplifying x + 0.5 = 0.75 Reorder the terms: 0.5 + x = 0.75 Solving 0.5 + x = 0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 0.75 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.75 + -0.5 x = 0.75 + -0.5 Combine like terms: 0.75 + -0.5 = 0.25 x = 0.25 Simplifying x = 0.25Subproblem 2
x + 0.5 = -0.75 Simplifying x + 0.5 = -0.75 Reorder the terms: 0.5 + x = -0.75 Solving 0.5 + x = -0.75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -0.75 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.75 + -0.5 x = -0.75 + -0.5 Combine like terms: -0.75 + -0.5 = -1.25 x = -1.25 Simplifying x = -1.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.25, -1.25}
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