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Simplifying x2 + 34x + -55 = 0 Reorder the terms: -55 + 34x + x2 = 0 Solving -55 + 34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 34x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + 34x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 34x + x2 = 0 + 55 34x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 34x + x2 = 55 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 = 55 + 289 Reorder the terms: 289 + 34x + x2 = 55 + 289 Combine like terms: 55 + 289 = 344 289 + 34x + x2 = 344 Factor a perfect square on the left side: (x + 17)(x + 17) = 344 Calculate the square root of the right side: 18.547236991 Break this problem into two subproblems by setting (x + 17) equal to 18.547236991 and -18.547236991.Subproblem 1
x + 17 = 18.547236991 Simplifying x + 17 = 18.547236991 Reorder the terms: 17 + x = 18.547236991 Solving 17 + x = 18.547236991 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 = 18.547236991 + -17 Combine like terms: 17 + -17 = 0 0 + x = 18.547236991 + -17 x = 18.547236991 + -17 Combine like terms: 18.547236991 + -17 = 1.547236991 x = 1.547236991 Simplifying x = 1.547236991Subproblem 2
x + 17 = -18.547236991 Simplifying x + 17 = -18.547236991 Reorder the terms: 17 + x = -18.547236991 Solving 17 + x = -18.547236991 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 = -18.547236991 + -17 Combine like terms: 17 + -17 = 0 0 + x = -18.547236991 + -17 x = -18.547236991 + -17 Combine like terms: -18.547236991 + -17 = -35.547236991 x = -35.547236991 Simplifying x = -35.547236991Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.547236991, -35.547236991}
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