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Simplifying x2 + -15x + -1024 = 0 Reorder the terms: -1024 + -15x + x2 = 0 Solving -1024 + -15x + 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 + -15x + 1024 + x2 = 0 + 1024 Reorder the terms: -1024 + 1024 + -15x + x2 = 0 + 1024 Combine like terms: -1024 + 1024 = 0 0 + -15x + x2 = 0 + 1024 -15x + x2 = 0 + 1024 Combine like terms: 0 + 1024 = 1024 -15x + x2 = 1024 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = 1024 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 1024 + 56.25 Combine like terms: 1024 + 56.25 = 1080.25 56.25 + -15x + x2 = 1080.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 1080.25 Calculate the square root of the right side: 32.867156859 Break this problem into two subproblems by setting (x + -7.5) equal to 32.867156859 and -32.867156859.Subproblem 1
x + -7.5 = 32.867156859 Simplifying x + -7.5 = 32.867156859 Reorder the terms: -7.5 + x = 32.867156859 Solving -7.5 + x = 32.867156859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 32.867156859 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 32.867156859 + 7.5 x = 32.867156859 + 7.5 Combine like terms: 32.867156859 + 7.5 = 40.367156859 x = 40.367156859 Simplifying x = 40.367156859Subproblem 2
x + -7.5 = -32.867156859 Simplifying x + -7.5 = -32.867156859 Reorder the terms: -7.5 + x = -32.867156859 Solving -7.5 + x = -32.867156859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -32.867156859 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -32.867156859 + 7.5 x = -32.867156859 + 7.5 Combine like terms: -32.867156859 + 7.5 = -25.367156859 x = -25.367156859 Simplifying x = -25.367156859Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.367156859, -25.367156859}
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