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Simplifying x2 + 42x + 377 = 64 Reorder the terms: 377 + 42x + x2 = 64 Solving 377 + 42x + x2 = 64 Solving for variable 'x'. Reorder the terms: 377 + -64 + 42x + x2 = 64 + -64 Combine like terms: 377 + -64 = 313 313 + 42x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 313 + 42x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-313' to each side of the equation. 313 + 42x + -313 + x2 = 0 + -313 Reorder the terms: 313 + -313 + 42x + x2 = 0 + -313 Combine like terms: 313 + -313 = 0 0 + 42x + x2 = 0 + -313 42x + x2 = 0 + -313 Combine like terms: 0 + -313 = -313 42x + x2 = -313 The x term is 42x. Take half its coefficient (21). Square it (441) and add it to both sides. Add '441' to each side of the equation. 42x + 441 + x2 = -313 + 441 Reorder the terms: 441 + 42x + x2 = -313 + 441 Combine like terms: -313 + 441 = 128 441 + 42x + x2 = 128 Factor a perfect square on the left side: (x + 21)(x + 21) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + 21) equal to 11.313708499 and -11.313708499.Subproblem 1
x + 21 = 11.313708499 Simplifying x + 21 = 11.313708499 Reorder the terms: 21 + x = 11.313708499 Solving 21 + x = 11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = 11.313708499 + -21 Combine like terms: 21 + -21 = 0 0 + x = 11.313708499 + -21 x = 11.313708499 + -21 Combine like terms: 11.313708499 + -21 = -9.686291501 x = -9.686291501 Simplifying x = -9.686291501Subproblem 2
x + 21 = -11.313708499 Simplifying x + 21 = -11.313708499 Reorder the terms: 21 + x = -11.313708499 Solving 21 + x = -11.313708499 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21' to each side of the equation. 21 + -21 + x = -11.313708499 + -21 Combine like terms: 21 + -21 = 0 0 + x = -11.313708499 + -21 x = -11.313708499 + -21 Combine like terms: -11.313708499 + -21 = -32.313708499 x = -32.313708499 Simplifying x = -32.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {-9.686291501, -32.313708499}
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