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Simplifying X2 + -8X + -792 = 0 Reorder the terms: -792 + -8X + X2 = 0 Solving -792 + -8X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '792' to each side of the equation. -792 + -8X + 792 + X2 = 0 + 792 Reorder the terms: -792 + 792 + -8X + X2 = 0 + 792 Combine like terms: -792 + 792 = 0 0 + -8X + X2 = 0 + 792 -8X + X2 = 0 + 792 Combine like terms: 0 + 792 = 792 -8X + X2 = 792 The X term is -8X. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8X + 16 + X2 = 792 + 16 Reorder the terms: 16 + -8X + X2 = 792 + 16 Combine like terms: 792 + 16 = 808 16 + -8X + X2 = 808 Factor a perfect square on the left side: (X + -4)(X + -4) = 808 Calculate the square root of the right side: 28.425340807 Break this problem into two subproblems by setting (X + -4) equal to 28.425340807 and -28.425340807.Subproblem 1
X + -4 = 28.425340807 Simplifying X + -4 = 28.425340807 Reorder the terms: -4 + X = 28.425340807 Solving -4 + X = 28.425340807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = 28.425340807 + 4 Combine like terms: -4 + 4 = 0 0 + X = 28.425340807 + 4 X = 28.425340807 + 4 Combine like terms: 28.425340807 + 4 = 32.425340807 X = 32.425340807 Simplifying X = 32.425340807Subproblem 2
X + -4 = -28.425340807 Simplifying X + -4 = -28.425340807 Reorder the terms: -4 + X = -28.425340807 Solving -4 + X = -28.425340807 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + X = -28.425340807 + 4 Combine like terms: -4 + 4 = 0 0 + X = -28.425340807 + 4 X = -28.425340807 + 4 Combine like terms: -28.425340807 + 4 = -24.425340807 X = -24.425340807 Simplifying X = -24.425340807Solution
The solution to the problem is based on the solutions from the subproblems. X = {32.425340807, -24.425340807}
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