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Simplifying x2 + 42x + 5 = 0 Reorder the terms: 5 + 42x + x2 = 0 Solving 5 + 42x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + 42x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 42x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 42x + x2 = 0 + -5 42x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 42x + x2 = -5 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 = -5 + 441 Reorder the terms: 441 + 42x + x2 = -5 + 441 Combine like terms: -5 + 441 = 436 441 + 42x + x2 = 436 Factor a perfect square on the left side: (x + 21)(x + 21) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (x + 21) equal to 20.880613018 and -20.880613018.Subproblem 1
x + 21 = 20.880613018 Simplifying x + 21 = 20.880613018 Reorder the terms: 21 + x = 20.880613018 Solving 21 + x = 20.880613018 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 = 20.880613018 + -21 Combine like terms: 21 + -21 = 0 0 + x = 20.880613018 + -21 x = 20.880613018 + -21 Combine like terms: 20.880613018 + -21 = -0.119386982 x = -0.119386982 Simplifying x = -0.119386982Subproblem 2
x + 21 = -20.880613018 Simplifying x + 21 = -20.880613018 Reorder the terms: 21 + x = -20.880613018 Solving 21 + x = -20.880613018 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 = -20.880613018 + -21 Combine like terms: 21 + -21 = 0 0 + x = -20.880613018 + -21 x = -20.880613018 + -21 Combine like terms: -20.880613018 + -21 = -41.880613018 x = -41.880613018 Simplifying x = -41.880613018Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.119386982, -41.880613018}
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