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Simplifying x2 + -17x + -180 = 0 Reorder the terms: -180 + -17x + x2 = 0 Solving -180 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + -17x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + -17x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + -17x + x2 = 0 + 180 -17x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 -17x + x2 = 180 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 = 180 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 180 + 72.25 Combine like terms: 180 + 72.25 = 252.25 72.25 + -17x + x2 = 252.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 252.25 Calculate the square root of the right side: 15.882380174 Break this problem into two subproblems by setting (x + -8.5) equal to 15.882380174 and -15.882380174.Subproblem 1
x + -8.5 = 15.882380174 Simplifying x + -8.5 = 15.882380174 Reorder the terms: -8.5 + x = 15.882380174 Solving -8.5 + x = 15.882380174 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 = 15.882380174 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 15.882380174 + 8.5 x = 15.882380174 + 8.5 Combine like terms: 15.882380174 + 8.5 = 24.382380174 x = 24.382380174 Simplifying x = 24.382380174Subproblem 2
x + -8.5 = -15.882380174 Simplifying x + -8.5 = -15.882380174 Reorder the terms: -8.5 + x = -15.882380174 Solving -8.5 + x = -15.882380174 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 = -15.882380174 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -15.882380174 + 8.5 x = -15.882380174 + 8.5 Combine like terms: -15.882380174 + 8.5 = -7.382380174 x = -7.382380174 Simplifying x = -7.382380174Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.382380174, -7.382380174}
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