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Simplifying x2 + 34x + 2 = 0 Reorder the terms: 2 + 34x + x2 = 0 Solving 2 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 34x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 34x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 34x + x2 = 0 + -2 34x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 34x + x2 = -2 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 = -2 + 289 Reorder the terms: 289 + 34x + x2 = -2 + 289 Combine like terms: -2 + 289 = 287 289 + 34x + x2 = 287 Factor a perfect square on the left side: (x + 17)(x + 17) = 287 Calculate the square root of the right side: 16.941074346 Break this problem into two subproblems by setting (x + 17) equal to 16.941074346 and -16.941074346.Subproblem 1
x + 17 = 16.941074346 Simplifying x + 17 = 16.941074346 Reorder the terms: 17 + x = 16.941074346 Solving 17 + x = 16.941074346 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 = 16.941074346 + -17 Combine like terms: 17 + -17 = 0 0 + x = 16.941074346 + -17 x = 16.941074346 + -17 Combine like terms: 16.941074346 + -17 = -0.058925654 x = -0.058925654 Simplifying x = -0.058925654Subproblem 2
x + 17 = -16.941074346 Simplifying x + 17 = -16.941074346 Reorder the terms: 17 + x = -16.941074346 Solving 17 + x = -16.941074346 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 = -16.941074346 + -17 Combine like terms: 17 + -17 = 0 0 + x = -16.941074346 + -17 x = -16.941074346 + -17 Combine like terms: -16.941074346 + -17 = -33.941074346 x = -33.941074346 Simplifying x = -33.941074346Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.058925654, -33.941074346}
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