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Simplifying x2 + -24x + -1024 = 0 Reorder the terms: -1024 + -24x + x2 = 0 Solving -1024 + -24x + 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 + -24x + 1024 + x2 = 0 + 1024 Reorder the terms: -1024 + 1024 + -24x + x2 = 0 + 1024 Combine like terms: -1024 + 1024 = 0 0 + -24x + x2 = 0 + 1024 -24x + x2 = 0 + 1024 Combine like terms: 0 + 1024 = 1024 -24x + x2 = 1024 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 1024 + 144 Reorder the terms: 144 + -24x + x2 = 1024 + 144 Combine like terms: 1024 + 144 = 1168 144 + -24x + x2 = 1168 Factor a perfect square on the left side: (x + -12)(x + -12) = 1168 Calculate the square root of the right side: 34.176014981 Break this problem into two subproblems by setting (x + -12) equal to 34.176014981 and -34.176014981.Subproblem 1
x + -12 = 34.176014981 Simplifying x + -12 = 34.176014981 Reorder the terms: -12 + x = 34.176014981 Solving -12 + x = 34.176014981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 34.176014981 + 12 Combine like terms: -12 + 12 = 0 0 + x = 34.176014981 + 12 x = 34.176014981 + 12 Combine like terms: 34.176014981 + 12 = 46.176014981 x = 46.176014981 Simplifying x = 46.176014981Subproblem 2
x + -12 = -34.176014981 Simplifying x + -12 = -34.176014981 Reorder the terms: -12 + x = -34.176014981 Solving -12 + x = -34.176014981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -34.176014981 + 12 Combine like terms: -12 + 12 = 0 0 + x = -34.176014981 + 12 x = -34.176014981 + 12 Combine like terms: -34.176014981 + 12 = -22.176014981 x = -22.176014981 Simplifying x = -22.176014981Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.176014981, -22.176014981}
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