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Simplifying x2 + -8x + 93x + -2 = 0 Reorder the terms: -2 + -8x + 93x + x2 = 0 Combine like terms: -8x + 93x = 85x -2 + 85x + x2 = 0 Solving -2 + 85x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 85x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 85x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 85x + x2 = 0 + 2 85x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 85x + x2 = 2 The x term is 85x. Take half its coefficient (42.5). Square it (1806.25) and add it to both sides. Add '1806.25' to each side of the equation. 85x + 1806.25 + x2 = 2 + 1806.25 Reorder the terms: 1806.25 + 85x + x2 = 2 + 1806.25 Combine like terms: 2 + 1806.25 = 1808.25 1806.25 + 85x + x2 = 1808.25 Factor a perfect square on the left side: (x + 42.5)(x + 42.5) = 1808.25 Calculate the square root of the right side: 42.523522902 Break this problem into two subproblems by setting (x + 42.5) equal to 42.523522902 and -42.523522902.Subproblem 1
x + 42.5 = 42.523522902 Simplifying x + 42.5 = 42.523522902 Reorder the terms: 42.5 + x = 42.523522902 Solving 42.5 + x = 42.523522902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + x = 42.523522902 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + x = 42.523522902 + -42.5 x = 42.523522902 + -42.5 Combine like terms: 42.523522902 + -42.5 = 0.023522902 x = 0.023522902 Simplifying x = 0.023522902Subproblem 2
x + 42.5 = -42.523522902 Simplifying x + 42.5 = -42.523522902 Reorder the terms: 42.5 + x = -42.523522902 Solving 42.5 + x = -42.523522902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42.5' to each side of the equation. 42.5 + -42.5 + x = -42.523522902 + -42.5 Combine like terms: 42.5 + -42.5 = 0.0 0.0 + x = -42.523522902 + -42.5 x = -42.523522902 + -42.5 Combine like terms: -42.523522902 + -42.5 = -85.023522902 x = -85.023522902 Simplifying x = -85.023522902Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.023522902, -85.023522902}
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