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Simplifying x2 + 21x + -184 = 0 Reorder the terms: -184 + 21x + x2 = 0 Solving -184 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '184' to each side of the equation. -184 + 21x + 184 + x2 = 0 + 184 Reorder the terms: -184 + 184 + 21x + x2 = 0 + 184 Combine like terms: -184 + 184 = 0 0 + 21x + x2 = 0 + 184 21x + x2 = 0 + 184 Combine like terms: 0 + 184 = 184 21x + x2 = 184 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 = 184 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 184 + 110.25 Combine like terms: 184 + 110.25 = 294.25 110.25 + 21x + x2 = 294.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 294.25 Calculate the square root of the right side: 17.153716798 Break this problem into two subproblems by setting (x + 10.5) equal to 17.153716798 and -17.153716798.Subproblem 1
x + 10.5 = 17.153716798 Simplifying x + 10.5 = 17.153716798 Reorder the terms: 10.5 + x = 17.153716798 Solving 10.5 + x = 17.153716798 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 = 17.153716798 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 17.153716798 + -10.5 x = 17.153716798 + -10.5 Combine like terms: 17.153716798 + -10.5 = 6.653716798 x = 6.653716798 Simplifying x = 6.653716798Subproblem 2
x + 10.5 = -17.153716798 Simplifying x + 10.5 = -17.153716798 Reorder the terms: 10.5 + x = -17.153716798 Solving 10.5 + x = -17.153716798 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 = -17.153716798 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -17.153716798 + -10.5 x = -17.153716798 + -10.5 Combine like terms: -17.153716798 + -10.5 = -27.653716798 x = -27.653716798 Simplifying x = -27.653716798Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.653716798, -27.653716798}
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