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Simplifying x2 + 642x + -639 = 0 Reorder the terms: -639 + 642x + x2 = 0 Solving -639 + 642x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '639' to each side of the equation. -639 + 642x + 639 + x2 = 0 + 639 Reorder the terms: -639 + 639 + 642x + x2 = 0 + 639 Combine like terms: -639 + 639 = 0 0 + 642x + x2 = 0 + 639 642x + x2 = 0 + 639 Combine like terms: 0 + 639 = 639 642x + x2 = 639 The x term is 642x. Take half its coefficient (321). Square it (103041) and add it to both sides. Add '103041' to each side of the equation. 642x + 103041 + x2 = 639 + 103041 Reorder the terms: 103041 + 642x + x2 = 639 + 103041 Combine like terms: 639 + 103041 = 103680 103041 + 642x + x2 = 103680 Factor a perfect square on the left side: (x + 321)(x + 321) = 103680 Calculate the square root of the right side: 321.99378876 Break this problem into two subproblems by setting (x + 321) equal to 321.99378876 and -321.99378876.Subproblem 1
x + 321 = 321.99378876 Simplifying x + 321 = 321.99378876 Reorder the terms: 321 + x = 321.99378876 Solving 321 + x = 321.99378876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-321' to each side of the equation. 321 + -321 + x = 321.99378876 + -321 Combine like terms: 321 + -321 = 0 0 + x = 321.99378876 + -321 x = 321.99378876 + -321 Combine like terms: 321.99378876 + -321 = 0.99378876 x = 0.99378876 Simplifying x = 0.99378876Subproblem 2
x + 321 = -321.99378876 Simplifying x + 321 = -321.99378876 Reorder the terms: 321 + x = -321.99378876 Solving 321 + x = -321.99378876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-321' to each side of the equation. 321 + -321 + x = -321.99378876 + -321 Combine like terms: 321 + -321 = 0 0 + x = -321.99378876 + -321 x = -321.99378876 + -321 Combine like terms: -321.99378876 + -321 = -642.99378876 x = -642.99378876 Simplifying x = -642.99378876Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.99378876, -642.99378876}
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