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Simplifying x2 + 21x + 31 = 0 Reorder the terms: 31 + 21x + x2 = 0 Solving 31 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 21x + -31 + x2 = 0 + -31 Reorder the terms: 31 + -31 + 21x + x2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 21x + x2 = 0 + -31 21x + x2 = 0 + -31 Combine like terms: 0 + -31 = -31 21x + x2 = -31 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -31 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -31 + 110.25 Combine like terms: -31 + 110.25 = 79.25 110.25 + 21x + x2 = 79.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 79.25 Calculate the square root of the right side: 8.902246907 Break this problem into two subproblems by setting (x + 10.5) equal to 8.902246907 and -8.902246907.Subproblem 1
x + 10.5 = 8.902246907 Simplifying x + 10.5 = 8.902246907 Reorder the terms: 10.5 + x = 8.902246907 Solving 10.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 8.902246907 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 8.902246907 + -10.5 x = 8.902246907 + -10.5 Combine like terms: 8.902246907 + -10.5 = -1.597753093 x = -1.597753093 Simplifying x = -1.597753093Subproblem 2
x + 10.5 = -8.902246907 Simplifying x + 10.5 = -8.902246907 Reorder the terms: 10.5 + x = -8.902246907 Solving 10.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -8.902246907 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -8.902246907 + -10.5 x = -8.902246907 + -10.5 Combine like terms: -8.902246907 + -10.5 = -19.402246907 x = -19.402246907 Simplifying x = -19.402246907Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.597753093, -19.402246907}
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