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Simplifying x * x + -17x + -17 = 0 Multiply x * x x2 + -17x + -17 = 0 Reorder the terms: -17 + -17x + x2 = 0 Solving -17 + -17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -17x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -17x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -17x + x2 = 0 + 17 -17x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -17x + x2 = 17 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 = 17 + 72.25 Reorder the terms: 72.25 + -17x + x2 = 17 + 72.25 Combine like terms: 17 + 72.25 = 89.25 72.25 + -17x + x2 = 89.25 Factor a perfect square on the left side: (x + -8.5)(x + -8.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + -8.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + -8.5 = 9.447221814 Simplifying x + -8.5 = 9.447221814 Reorder the terms: -8.5 + x = 9.447221814 Solving -8.5 + x = 9.447221814 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 = 9.447221814 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.447221814 + 8.5 x = 9.447221814 + 8.5 Combine like terms: 9.447221814 + 8.5 = 17.947221814 x = 17.947221814 Simplifying x = 17.947221814Subproblem 2
x + -8.5 = -9.447221814 Simplifying x + -8.5 = -9.447221814 Reorder the terms: -8.5 + x = -9.447221814 Solving -8.5 + x = -9.447221814 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 = -9.447221814 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.447221814 + 8.5 x = -9.447221814 + 8.5 Combine like terms: -9.447221814 + 8.5 = -0.947221814 x = -0.947221814 Simplifying x = -0.947221814Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.947221814, -0.947221814}
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