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Simplifying x2 + 34x + 275 = 0 Reorder the terms: 275 + 34x + x2 = 0 Solving 275 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-275' to each side of the equation. 275 + 34x + -275 + x2 = 0 + -275 Reorder the terms: 275 + -275 + 34x + x2 = 0 + -275 Combine like terms: 275 + -275 = 0 0 + 34x + x2 = 0 + -275 34x + x2 = 0 + -275 Combine like terms: 0 + -275 = -275 34x + x2 = -275 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 = -275 + 289 Reorder the terms: 289 + 34x + x2 = -275 + 289 Combine like terms: -275 + 289 = 14 289 + 34x + x2 = 14 Factor a perfect square on the left side: (x + 17)(x + 17) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 17) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 17 = 3.741657387 Simplifying x + 17 = 3.741657387 Reorder the terms: 17 + x = 3.741657387 Solving 17 + x = 3.741657387 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 = 3.741657387 + -17 Combine like terms: 17 + -17 = 0 0 + x = 3.741657387 + -17 x = 3.741657387 + -17 Combine like terms: 3.741657387 + -17 = -13.258342613 x = -13.258342613 Simplifying x = -13.258342613Subproblem 2
x + 17 = -3.741657387 Simplifying x + 17 = -3.741657387 Reorder the terms: 17 + x = -3.741657387 Solving 17 + x = -3.741657387 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 = -3.741657387 + -17 Combine like terms: 17 + -17 = 0 0 + x = -3.741657387 + -17 x = -3.741657387 + -17 Combine like terms: -3.741657387 + -17 = -20.741657387 x = -20.741657387 Simplifying x = -20.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.258342613, -20.741657387}
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