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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 = 323 289 + 34x + x2 = 323 Factor a perfect square on the left side: (x + 17)(x + 17) = 323 Calculate the square root of the right side: 17.972200756 Break this problem into two subproblems by setting (x + 17) equal to 17.972200756 and -17.972200756.Subproblem 1
x + 17 = 17.972200756 Simplifying x + 17 = 17.972200756 Reorder the terms: 17 + x = 17.972200756 Solving 17 + x = 17.972200756 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 = 17.972200756 + -17 Combine like terms: 17 + -17 = 0 0 + x = 17.972200756 + -17 x = 17.972200756 + -17 Combine like terms: 17.972200756 + -17 = 0.972200756 x = 0.972200756 Simplifying x = 0.972200756Subproblem 2
x + 17 = -17.972200756 Simplifying x + 17 = -17.972200756 Reorder the terms: 17 + x = -17.972200756 Solving 17 + x = -17.972200756 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 = -17.972200756 + -17 Combine like terms: 17 + -17 = 0 0 + x = -17.972200756 + -17 x = -17.972200756 + -17 Combine like terms: -17.972200756 + -17 = -34.972200756 x = -34.972200756 Simplifying x = -34.972200756Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.972200756, -34.972200756}
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