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Simplifying x2 + 42x + 39 = 0 Reorder the terms: 39 + 42x + x2 = 0 Solving 39 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 42x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 42x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 42x + x2 = 0 + -39 42x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 42x + x2 = -39 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 = -39 + 441 Reorder the terms: 441 + 42x + x2 = -39 + 441 Combine like terms: -39 + 441 = 402 441 + 42x + x2 = 402 Factor a perfect square on the left side: (x + 21)(x + 21) = 402 Calculate the square root of the right side: 20.049937656 Break this problem into two subproblems by setting (x + 21) equal to 20.049937656 and -20.049937656.Subproblem 1
x + 21 = 20.049937656 Simplifying x + 21 = 20.049937656 Reorder the terms: 21 + x = 20.049937656 Solving 21 + x = 20.049937656 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 = 20.049937656 + -21 Combine like terms: 21 + -21 = 0 0 + x = 20.049937656 + -21 x = 20.049937656 + -21 Combine like terms: 20.049937656 + -21 = -0.950062344 x = -0.950062344 Simplifying x = -0.950062344Subproblem 2
x + 21 = -20.049937656 Simplifying x + 21 = -20.049937656 Reorder the terms: 21 + x = -20.049937656 Solving 21 + x = -20.049937656 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 = -20.049937656 + -21 Combine like terms: 21 + -21 = 0 0 + x = -20.049937656 + -21 x = -20.049937656 + -21 Combine like terms: -20.049937656 + -21 = -41.049937656 x = -41.049937656 Simplifying x = -41.049937656Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.950062344, -41.049937656}
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