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Simplifying x2 + 42x + 60 = 0 Reorder the terms: 60 + 42x + x2 = 0 Solving 60 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + 42x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 42x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 42x + x2 = 0 + -60 42x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 42x + x2 = -60 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 = -60 + 441 Reorder the terms: 441 + 42x + x2 = -60 + 441 Combine like terms: -60 + 441 = 381 441 + 42x + x2 = 381 Factor a perfect square on the left side: (x + 21)(x + 21) = 381 Calculate the square root of the right side: 19.519221296 Break this problem into two subproblems by setting (x + 21) equal to 19.519221296 and -19.519221296.Subproblem 1
x + 21 = 19.519221296 Simplifying x + 21 = 19.519221296 Reorder the terms: 21 + x = 19.519221296 Solving 21 + x = 19.519221296 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 = 19.519221296 + -21 Combine like terms: 21 + -21 = 0 0 + x = 19.519221296 + -21 x = 19.519221296 + -21 Combine like terms: 19.519221296 + -21 = -1.480778704 x = -1.480778704 Simplifying x = -1.480778704Subproblem 2
x + 21 = -19.519221296 Simplifying x + 21 = -19.519221296 Reorder the terms: 21 + x = -19.519221296 Solving 21 + x = -19.519221296 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 = -19.519221296 + -21 Combine like terms: 21 + -21 = 0 0 + x = -19.519221296 + -21 x = -19.519221296 + -21 Combine like terms: -19.519221296 + -21 = -40.519221296 x = -40.519221296 Simplifying x = -40.519221296Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.480778704, -40.519221296}
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