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Simplifying x2 + 17x + -42 = 0 Reorder the terms: -42 + 17x + x2 = 0 Solving -42 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + 17x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + 17x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + 17x + x2 = 0 + 42 17x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 17x + x2 = 42 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 42 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 42 + 72.25 Combine like terms: 42 + 72.25 = 114.25 72.25 + 17x + x2 = 114.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + 8.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + 8.5 = 10.688779163 Simplifying x + 8.5 = 10.688779163 Reorder the terms: 8.5 + x = 10.688779163 Solving 8.5 + x = 10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 10.688779163 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 10.688779163 + -8.5 x = 10.688779163 + -8.5 Combine like terms: 10.688779163 + -8.5 = 2.188779163 x = 2.188779163 Simplifying x = 2.188779163Subproblem 2
x + 8.5 = -10.688779163 Simplifying x + 8.5 = -10.688779163 Reorder the terms: 8.5 + x = -10.688779163 Solving 8.5 + x = -10.688779163 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -10.688779163 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -10.688779163 + -8.5 x = -10.688779163 + -8.5 Combine like terms: -10.688779163 + -8.5 = -19.188779163 x = -19.188779163 Simplifying x = -19.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.188779163, -19.188779163}
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