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Simplifying x2 + -17x + -5 = 0 Reorder the terms: -5 + -17x + x2 = 0 Solving -5 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -17x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -17x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -17x + x2 = 0 + 5 -17x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -17x + x2 = 5 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 = 5 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 5 + 72.25 Combine like terms: 5 + 72.25 = 77.25 72.25 + -17x + x2 = 77.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (x + -8.5) equal to 8.789197916 and -8.789197916.Subproblem 1
x + -8.5 = 8.789197916 Simplifying x + -8.5 = 8.789197916 Reorder the terms: -8.5 + x = 8.789197916 Solving -8.5 + x = 8.789197916 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 = 8.789197916 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.789197916 + 8.5 x = 8.789197916 + 8.5 Combine like terms: 8.789197916 + 8.5 = 17.289197916 x = 17.289197916 Simplifying x = 17.289197916Subproblem 2
x + -8.5 = -8.789197916 Simplifying x + -8.5 = -8.789197916 Reorder the terms: -8.5 + x = -8.789197916 Solving -8.5 + x = -8.789197916 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 = -8.789197916 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.789197916 + 8.5 x = -8.789197916 + 8.5 Combine like terms: -8.789197916 + 8.5 = -0.289197916 x = -0.289197916 Simplifying x = -0.289197916Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.289197916, -0.289197916}
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