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Simplifying -1x2 + 17x + 42 = 0 Reorder the terms: 42 + 17x + -1x2 = 0 Solving 42 + 17x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -42 + -17x + x2 = 0 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 = 19.188779163 x = 19.188779163 Simplifying x = 19.188779163Subproblem 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 = -2.188779163 x = -2.188779163 Simplifying x = -2.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.188779163, -2.188779163}
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