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Simplifying x2 + 21x + 21 = 0 Reorder the terms: 21 + 21x + x2 = 0 Solving 21 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 21x + -21 + x2 = 0 + -21 Reorder the terms: 21 + -21 + 21x + x2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 21x + x2 = 0 + -21 21x + x2 = 0 + -21 Combine like terms: 0 + -21 = -21 21x + x2 = -21 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 = -21 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -21 + 110.25 Combine like terms: -21 + 110.25 = 89.25 110.25 + 21x + x2 = 89.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 89.25 Calculate the square root of the right side: 9.447221814 Break this problem into two subproblems by setting (x + 10.5) equal to 9.447221814 and -9.447221814.Subproblem 1
x + 10.5 = 9.447221814 Simplifying x + 10.5 = 9.447221814 Reorder the terms: 10.5 + x = 9.447221814 Solving 10.5 + x = 9.447221814 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 = 9.447221814 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 9.447221814 + -10.5 x = 9.447221814 + -10.5 Combine like terms: 9.447221814 + -10.5 = -1.052778186 x = -1.052778186 Simplifying x = -1.052778186Subproblem 2
x + 10.5 = -9.447221814 Simplifying x + 10.5 = -9.447221814 Reorder the terms: 10.5 + x = -9.447221814 Solving 10.5 + x = -9.447221814 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 = -9.447221814 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -9.447221814 + -10.5 x = -9.447221814 + -10.5 Combine like terms: -9.447221814 + -10.5 = -19.947221814 x = -19.947221814 Simplifying x = -19.947221814Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.052778186, -19.947221814}
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