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Simplifying x2 + -34x + 209 = 0 Reorder the terms: 209 + -34x + x2 = 0 Solving 209 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-209' to each side of the equation. 209 + -34x + -209 + x2 = 0 + -209 Reorder the terms: 209 + -209 + -34x + x2 = 0 + -209 Combine like terms: 209 + -209 = 0 0 + -34x + x2 = 0 + -209 -34x + x2 = 0 + -209 Combine like terms: 0 + -209 = -209 -34x + x2 = -209 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -209 + 289 Reorder the terms: 289 + -34x + x2 = -209 + 289 Combine like terms: -209 + 289 = 80 289 + -34x + x2 = 80 Factor a perfect square on the left side: (x + -17)(x + -17) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -17) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -17 = 8.94427191 Simplifying x + -17 = 8.94427191 Reorder the terms: -17 + x = 8.94427191 Solving -17 + x = 8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 8.94427191 + 17 Combine like terms: -17 + 17 = 0 0 + x = 8.94427191 + 17 x = 8.94427191 + 17 Combine like terms: 8.94427191 + 17 = 25.94427191 x = 25.94427191 Simplifying x = 25.94427191Subproblem 2
x + -17 = -8.94427191 Simplifying x + -17 = -8.94427191 Reorder the terms: -17 + x = -8.94427191 Solving -17 + x = -8.94427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -8.94427191 + 17 Combine like terms: -17 + 17 = 0 0 + x = -8.94427191 + 17 x = -8.94427191 + 17 Combine like terms: -8.94427191 + 17 = 8.05572809 x = 8.05572809 Simplifying x = 8.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.94427191, 8.05572809}
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