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Simplifying 0.25 = 8(x2) + 2x + -5 Reorder the terms: 0.25 = -5 + 2x + 8x2 Solving 0.25 = -5 + 2x + 8x2 Solving for variable 'x'. Combine like terms: 0.25 + 5 = 5.25 5.25 + -2x + -8x2 = -5 + 2x + 8x2 + 5 + -2x + -8x2 Reorder the terms: 5.25 + -2x + -8x2 = -5 + 5 + 2x + -2x + 8x2 + -8x2 Combine like terms: -5 + 5 = 0 5.25 + -2x + -8x2 = 0 + 2x + -2x + 8x2 + -8x2 5.25 + -2x + -8x2 = 2x + -2x + 8x2 + -8x2 Combine like terms: 2x + -2x = 0 5.25 + -2x + -8x2 = 0 + 8x2 + -8x2 5.25 + -2x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 5.25 + -2x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.65625 + 0.25x + x2 = 0 Move the constant term to the right: Add '0.65625' to each side of the equation. -0.65625 + 0.25x + 0.65625 + x2 = 0 + 0.65625 Reorder the terms: -0.65625 + 0.65625 + 0.25x + x2 = 0 + 0.65625 Combine like terms: -0.65625 + 0.65625 = 0.00000 0.00000 + 0.25x + x2 = 0 + 0.65625 0.25x + x2 = 0 + 0.65625 Combine like terms: 0 + 0.65625 = 0.65625 0.25x + x2 = 0.65625 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 = 0.65625 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 0.65625 + 0.015625 Combine like terms: 0.65625 + 0.015625 = 0.671875 0.015625 + 0.25x + x2 = 0.671875 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 0.671875 Calculate the square root of the right side: 0.819679816 Break this problem into two subproblems by setting (x + 0.125) equal to 0.819679816 and -0.819679816.Subproblem 1
x + 0.125 = 0.819679816 Simplifying x + 0.125 = 0.819679816 Reorder the terms: 0.125 + x = 0.819679816 Solving 0.125 + x = 0.819679816 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 = 0.819679816 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 0.819679816 + -0.125 x = 0.819679816 + -0.125 Combine like terms: 0.819679816 + -0.125 = 0.694679816 x = 0.694679816 Simplifying x = 0.694679816Subproblem 2
x + 0.125 = -0.819679816 Simplifying x + 0.125 = -0.819679816 Reorder the terms: 0.125 + x = -0.819679816 Solving 0.125 + x = -0.819679816 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 = -0.819679816 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -0.819679816 + -0.125 x = -0.819679816 + -0.125 Combine like terms: -0.819679816 + -0.125 = -0.944679816 x = -0.944679816 Simplifying x = -0.944679816Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.694679816, -0.944679816}
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