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Simplifying 8x2 + 31x + 2 = 0 Reorder the terms: 2 + 31x + 8x2 = 0 Solving 2 + 31x + 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'. 0.25 + 3.875x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 3.875x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 3.875x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 3.875x + x2 = 0 + -0.25 3.875x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 3.875x + x2 = -0.25 The x term is 3.875x. Take half its coefficient (1.9375). Square it (3.75390625) and add it to both sides. Add '3.75390625' to each side of the equation. 3.875x + 3.75390625 + x2 = -0.25 + 3.75390625 Reorder the terms: 3.75390625 + 3.875x + x2 = -0.25 + 3.75390625 Combine like terms: -0.25 + 3.75390625 = 3.50390625 3.75390625 + 3.875x + x2 = 3.50390625 Factor a perfect square on the left side: (x + 1.9375)(x + 1.9375) = 3.50390625 Calculate the square root of the right side: 1.871872391 Break this problem into two subproblems by setting (x + 1.9375) equal to 1.871872391 and -1.871872391.Subproblem 1
x + 1.9375 = 1.871872391 Simplifying x + 1.9375 = 1.871872391 Reorder the terms: 1.9375 + x = 1.871872391 Solving 1.9375 + x = 1.871872391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = 1.871872391 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = 1.871872391 + -1.9375 x = 1.871872391 + -1.9375 Combine like terms: 1.871872391 + -1.9375 = -0.065627609 x = -0.065627609 Simplifying x = -0.065627609Subproblem 2
x + 1.9375 = -1.871872391 Simplifying x + 1.9375 = -1.871872391 Reorder the terms: 1.9375 + x = -1.871872391 Solving 1.9375 + x = -1.871872391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9375' to each side of the equation. 1.9375 + -1.9375 + x = -1.871872391 + -1.9375 Combine like terms: 1.9375 + -1.9375 = 0.0000 0.0000 + x = -1.871872391 + -1.9375 x = -1.871872391 + -1.9375 Combine like terms: -1.871872391 + -1.9375 = -3.809372391 x = -3.809372391 Simplifying x = -3.809372391Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.065627609, -3.809372391}
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