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Simplifying (X + 5)(X + 5) = 80 Reorder the terms: (5 + X)(X + 5) = 80 Reorder the terms: (5 + X)(5 + X) = 80 Multiply (5 + X) * (5 + X) (5(5 + X) + X(5 + X)) = 80 ((5 * 5 + X * 5) + X(5 + X)) = 80 ((25 + 5X) + X(5 + X)) = 80 (25 + 5X + (5 * X + X * X)) = 80 (25 + 5X + (5X + X2)) = 80 Combine like terms: 5X + 5X = 10X (25 + 10X + X2) = 80 Solving 25 + 10X + X2 = 80 Solving for variable 'X'. Reorder the terms: 25 + -80 + 10X + X2 = 80 + -80 Combine like terms: 25 + -80 = -55 -55 + 10X + X2 = 80 + -80 Combine like terms: 80 + -80 = 0 -55 + 10X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 10X + 55 + X2 = 0 + 55 Reorder the terms: -55 + 55 + 10X + X2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 10X + X2 = 0 + 55 10X + X2 = 0 + 55 Combine like terms: 0 + 55 = 55 10X + X2 = 55 The X term is 10X. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10X + 25 + X2 = 55 + 25 Reorder the terms: 25 + 10X + X2 = 55 + 25 Combine like terms: 55 + 25 = 80 25 + 10X + X2 = 80 Factor a perfect square on the left side: (X + 5)(X + 5) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (X + 5) equal to 8.94427191 and -8.94427191.Subproblem 1
X + 5 = 8.94427191 Simplifying X + 5 = 8.94427191 Reorder the terms: 5 + X = 8.94427191 Solving 5 + X = 8.94427191 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = 8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + X = 8.94427191 + -5 X = 8.94427191 + -5 Combine like terms: 8.94427191 + -5 = 3.94427191 X = 3.94427191 Simplifying X = 3.94427191Subproblem 2
X + 5 = -8.94427191 Simplifying X + 5 = -8.94427191 Reorder the terms: 5 + X = -8.94427191 Solving 5 + X = -8.94427191 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + X = -8.94427191 + -5 Combine like terms: 5 + -5 = 0 0 + X = -8.94427191 + -5 X = -8.94427191 + -5 Combine like terms: -8.94427191 + -5 = -13.94427191 X = -13.94427191 Simplifying X = -13.94427191Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.94427191, -13.94427191}
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