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Simplifying x2 + 34x + 34 = 0 Reorder the terms: 34 + 34x + x2 = 0 Solving 34 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + 34x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 34x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 34x + x2 = 0 + -34 34x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 34x + x2 = -34 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 = -34 + 289 Reorder the terms: 289 + 34x + x2 = -34 + 289 Combine like terms: -34 + 289 = 255 289 + 34x + x2 = 255 Factor a perfect square on the left side: (x + 17)(x + 17) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (x + 17) equal to 15.968719423 and -15.968719423.Subproblem 1
x + 17 = 15.968719423 Simplifying x + 17 = 15.968719423 Reorder the terms: 17 + x = 15.968719423 Solving 17 + x = 15.968719423 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 = 15.968719423 + -17 Combine like terms: 17 + -17 = 0 0 + x = 15.968719423 + -17 x = 15.968719423 + -17 Combine like terms: 15.968719423 + -17 = -1.031280577 x = -1.031280577 Simplifying x = -1.031280577Subproblem 2
x + 17 = -15.968719423 Simplifying x + 17 = -15.968719423 Reorder the terms: 17 + x = -15.968719423 Solving 17 + x = -15.968719423 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 = -15.968719423 + -17 Combine like terms: 17 + -17 = 0 0 + x = -15.968719423 + -17 x = -15.968719423 + -17 Combine like terms: -15.968719423 + -17 = -32.968719423 x = -32.968719423 Simplifying x = -32.968719423Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.031280577, -32.968719423}
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