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Simplifying x2 + -16x + -1024 = 0 Reorder the terms: -1024 + -16x + x2 = 0 Solving -1024 + -16x + 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 + -16x + 1024 + x2 = 0 + 1024 Reorder the terms: -1024 + 1024 + -16x + x2 = 0 + 1024 Combine like terms: -1024 + 1024 = 0 0 + -16x + x2 = 0 + 1024 -16x + x2 = 0 + 1024 Combine like terms: 0 + 1024 = 1024 -16x + x2 = 1024 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 1024 + 64 Reorder the terms: 64 + -16x + x2 = 1024 + 64 Combine like terms: 1024 + 64 = 1088 64 + -16x + x2 = 1088 Factor a perfect square on the left side: (x + -8)(x + -8) = 1088 Calculate the square root of the right side: 32.984845005 Break this problem into two subproblems by setting (x + -8) equal to 32.984845005 and -32.984845005.Subproblem 1
x + -8 = 32.984845005 Simplifying x + -8 = 32.984845005 Reorder the terms: -8 + x = 32.984845005 Solving -8 + x = 32.984845005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 32.984845005 + 8 Combine like terms: -8 + 8 = 0 0 + x = 32.984845005 + 8 x = 32.984845005 + 8 Combine like terms: 32.984845005 + 8 = 40.984845005 x = 40.984845005 Simplifying x = 40.984845005Subproblem 2
x + -8 = -32.984845005 Simplifying x + -8 = -32.984845005 Reorder the terms: -8 + x = -32.984845005 Solving -8 + x = -32.984845005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -32.984845005 + 8 Combine like terms: -8 + 8 = 0 0 + x = -32.984845005 + 8 x = -32.984845005 + 8 Combine like terms: -32.984845005 + 8 = -24.984845005 x = -24.984845005 Simplifying x = -24.984845005Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.984845005, -24.984845005}
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