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Simplifying x2 + -34x + -120 = 0 Reorder the terms: -120 + -34x + x2 = 0 Solving -120 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -34x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -34x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -34x + x2 = 0 + 120 -34x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -34x + x2 = 120 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 = 120 + 289 Reorder the terms: 289 + -34x + x2 = 120 + 289 Combine like terms: 120 + 289 = 409 289 + -34x + x2 = 409 Factor a perfect square on the left side: (x + -17)(x + -17) = 409 Calculate the square root of the right side: 20.223748416 Break this problem into two subproblems by setting (x + -17) equal to 20.223748416 and -20.223748416.Subproblem 1
x + -17 = 20.223748416 Simplifying x + -17 = 20.223748416 Reorder the terms: -17 + x = 20.223748416 Solving -17 + x = 20.223748416 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 = 20.223748416 + 17 Combine like terms: -17 + 17 = 0 0 + x = 20.223748416 + 17 x = 20.223748416 + 17 Combine like terms: 20.223748416 + 17 = 37.223748416 x = 37.223748416 Simplifying x = 37.223748416Subproblem 2
x + -17 = -20.223748416 Simplifying x + -17 = -20.223748416 Reorder the terms: -17 + x = -20.223748416 Solving -17 + x = -20.223748416 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 = -20.223748416 + 17 Combine like terms: -17 + 17 = 0 0 + x = -20.223748416 + 17 x = -20.223748416 + 17 Combine like terms: -20.223748416 + 17 = -3.223748416 x = -3.223748416 Simplifying x = -3.223748416Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.223748416, -3.223748416}
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