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Simplifying x2 + -34x + 9 = 0 Reorder the terms: 9 + -34x + x2 = 0 Solving 9 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -34x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -34x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -34x + x2 = 0 + -9 -34x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -34x + x2 = -9 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 = -9 + 289 Reorder the terms: 289 + -34x + x2 = -9 + 289 Combine like terms: -9 + 289 = 280 289 + -34x + x2 = 280 Factor a perfect square on the left side: (x + -17)(x + -17) = 280 Calculate the square root of the right side: 16.733200531 Break this problem into two subproblems by setting (x + -17) equal to 16.733200531 and -16.733200531.Subproblem 1
x + -17 = 16.733200531 Simplifying x + -17 = 16.733200531 Reorder the terms: -17 + x = 16.733200531 Solving -17 + x = 16.733200531 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 = 16.733200531 + 17 Combine like terms: -17 + 17 = 0 0 + x = 16.733200531 + 17 x = 16.733200531 + 17 Combine like terms: 16.733200531 + 17 = 33.733200531 x = 33.733200531 Simplifying x = 33.733200531Subproblem 2
x + -17 = -16.733200531 Simplifying x + -17 = -16.733200531 Reorder the terms: -17 + x = -16.733200531 Solving -17 + x = -16.733200531 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 = -16.733200531 + 17 Combine like terms: -17 + 17 = 0 0 + x = -16.733200531 + 17 x = -16.733200531 + 17 Combine like terms: -16.733200531 + 17 = 0.266799469 x = 0.266799469 Simplifying x = 0.266799469Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.733200531, 0.266799469}
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