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Simplifying 8x2 + 2x + -211 = 0 Reorder the terms: -211 + 2x + 8x2 = 0 Solving -211 + 2x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -26.375 + 0.25x + x2 = 0 Move the constant term to the right: Add '26.375' to each side of the equation. -26.375 + 0.25x + 26.375 + x2 = 0 + 26.375 Reorder the terms: -26.375 + 26.375 + 0.25x + x2 = 0 + 26.375 Combine like terms: -26.375 + 26.375 = 0.000 0.000 + 0.25x + x2 = 0 + 26.375 0.25x + x2 = 0 + 26.375 Combine like terms: 0 + 26.375 = 26.375 0.25x + x2 = 26.375 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 = 26.375 + 0.015625 Reorder the terms: 0.015625 + 0.25x + x2 = 26.375 + 0.015625 Combine like terms: 26.375 + 0.015625 = 26.390625 0.015625 + 0.25x + x2 = 26.390625 Factor a perfect square on the left side: (x + 0.125)(x + 0.125) = 26.390625 Calculate the square root of the right side: 5.137180647 Break this problem into two subproblems by setting (x + 0.125) equal to 5.137180647 and -5.137180647.Subproblem 1
x + 0.125 = 5.137180647 Simplifying x + 0.125 = 5.137180647 Reorder the terms: 0.125 + x = 5.137180647 Solving 0.125 + x = 5.137180647 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 = 5.137180647 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = 5.137180647 + -0.125 x = 5.137180647 + -0.125 Combine like terms: 5.137180647 + -0.125 = 5.012180647 x = 5.012180647 Simplifying x = 5.012180647Subproblem 2
x + 0.125 = -5.137180647 Simplifying x + 0.125 = -5.137180647 Reorder the terms: 0.125 + x = -5.137180647 Solving 0.125 + x = -5.137180647 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 = -5.137180647 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + x = -5.137180647 + -0.125 x = -5.137180647 + -0.125 Combine like terms: -5.137180647 + -0.125 = -5.262180647 x = -5.262180647 Simplifying x = -5.262180647Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.012180647, -5.262180647}
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