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Simplifying x2 + 34x + 35 = 0 Reorder the terms: 35 + 34x + x2 = 0 Solving 35 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 34x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 34x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 34x + x2 = 0 + -35 34x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 34x + x2 = -35 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 = -35 + 289 Reorder the terms: 289 + 34x + x2 = -35 + 289 Combine like terms: -35 + 289 = 254 289 + 34x + x2 = 254 Factor a perfect square on the left side: (x + 17)(x + 17) = 254 Calculate the square root of the right side: 15.937377451 Break this problem into two subproblems by setting (x + 17) equal to 15.937377451 and -15.937377451.Subproblem 1
x + 17 = 15.937377451 Simplifying x + 17 = 15.937377451 Reorder the terms: 17 + x = 15.937377451 Solving 17 + x = 15.937377451 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 = 15.937377451 + -17 Combine like terms: 17 + -17 = 0 0 + x = 15.937377451 + -17 x = 15.937377451 + -17 Combine like terms: 15.937377451 + -17 = -1.062622549 x = -1.062622549 Simplifying x = -1.062622549Subproblem 2
x + 17 = -15.937377451 Simplifying x + 17 = -15.937377451 Reorder the terms: 17 + x = -15.937377451 Solving 17 + x = -15.937377451 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 = -15.937377451 + -17 Combine like terms: 17 + -17 = 0 0 + x = -15.937377451 + -17 x = -15.937377451 + -17 Combine like terms: -15.937377451 + -17 = -32.937377451 x = -32.937377451 Simplifying x = -32.937377451Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.062622549, -32.937377451}
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