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Simplifying x2 + 21x + -1024 = 0 Reorder the terms: -1024 + 21x + x2 = 0 Solving -1024 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1024' to each side of the equation. -1024 + 21x + 1024 + x2 = 0 + 1024 Reorder the terms: -1024 + 1024 + 21x + x2 = 0 + 1024 Combine like terms: -1024 + 1024 = 0 0 + 21x + x2 = 0 + 1024 21x + x2 = 0 + 1024 Combine like terms: 0 + 1024 = 1024 21x + x2 = 1024 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 = 1024 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 1024 + 110.25 Combine like terms: 1024 + 110.25 = 1134.25 110.25 + 21x + x2 = 1134.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 1134.25 Calculate the square root of the right side: 33.678628238 Break this problem into two subproblems by setting (x + 10.5) equal to 33.678628238 and -33.678628238.Subproblem 1
x + 10.5 = 33.678628238 Simplifying x + 10.5 = 33.678628238 Reorder the terms: 10.5 + x = 33.678628238 Solving 10.5 + x = 33.678628238 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 = 33.678628238 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 33.678628238 + -10.5 x = 33.678628238 + -10.5 Combine like terms: 33.678628238 + -10.5 = 23.178628238 x = 23.178628238 Simplifying x = 23.178628238Subproblem 2
x + 10.5 = -33.678628238 Simplifying x + 10.5 = -33.678628238 Reorder the terms: 10.5 + x = -33.678628238 Solving 10.5 + x = -33.678628238 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 = -33.678628238 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -33.678628238 + -10.5 x = -33.678628238 + -10.5 Combine like terms: -33.678628238 + -10.5 = -44.178628238 x = -44.178628238 Simplifying x = -44.178628238Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.178628238, -44.178628238}
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