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Simplifying x2 + 42x + -396 = 0 Reorder the terms: -396 + 42x + x2 = 0 Solving -396 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '396' to each side of the equation. -396 + 42x + 396 + x2 = 0 + 396 Reorder the terms: -396 + 396 + 42x + x2 = 0 + 396 Combine like terms: -396 + 396 = 0 0 + 42x + x2 = 0 + 396 42x + x2 = 0 + 396 Combine like terms: 0 + 396 = 396 42x + x2 = 396 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 = 396 + 441 Reorder the terms: 441 + 42x + x2 = 396 + 441 Combine like terms: 396 + 441 = 837 441 + 42x + x2 = 837 Factor a perfect square on the left side: (x + 21)(x + 21) = 837 Calculate the square root of the right side: 28.930952283 Break this problem into two subproblems by setting (x + 21) equal to 28.930952283 and -28.930952283.Subproblem 1
x + 21 = 28.930952283 Simplifying x + 21 = 28.930952283 Reorder the terms: 21 + x = 28.930952283 Solving 21 + x = 28.930952283 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 = 28.930952283 + -21 Combine like terms: 21 + -21 = 0 0 + x = 28.930952283 + -21 x = 28.930952283 + -21 Combine like terms: 28.930952283 + -21 = 7.930952283 x = 7.930952283 Simplifying x = 7.930952283Subproblem 2
x + 21 = -28.930952283 Simplifying x + 21 = -28.930952283 Reorder the terms: 21 + x = -28.930952283 Solving 21 + x = -28.930952283 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 = -28.930952283 + -21 Combine like terms: 21 + -21 = 0 0 + x = -28.930952283 + -21 x = -28.930952283 + -21 Combine like terms: -28.930952283 + -21 = -49.930952283 x = -49.930952283 Simplifying x = -49.930952283Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.930952283, -49.930952283}
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