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Simplifying x2 + 17x + 7 = 0 Reorder the terms: 7 + 17x + x2 = 0 Solving 7 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 17x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 17x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 17x + x2 = 0 + -7 17x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 17x + x2 = -7 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 = -7 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -7 + 72.25 Combine like terms: -7 + 72.25 = 65.25 72.25 + 17x + x2 = 65.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (x + 8.5) equal to 8.077747211 and -8.077747211.Subproblem 1
x + 8.5 = 8.077747211 Simplifying x + 8.5 = 8.077747211 Reorder the terms: 8.5 + x = 8.077747211 Solving 8.5 + x = 8.077747211 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 = 8.077747211 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 8.077747211 + -8.5 x = 8.077747211 + -8.5 Combine like terms: 8.077747211 + -8.5 = -0.422252789 x = -0.422252789 Simplifying x = -0.422252789Subproblem 2
x + 8.5 = -8.077747211 Simplifying x + 8.5 = -8.077747211 Reorder the terms: 8.5 + x = -8.077747211 Solving 8.5 + x = -8.077747211 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 = -8.077747211 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -8.077747211 + -8.5 x = -8.077747211 + -8.5 Combine like terms: -8.077747211 + -8.5 = -16.577747211 x = -16.577747211 Simplifying x = -16.577747211Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.422252789, -16.577747211}
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