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Simplifying (X + -5)(X + 9) = 175 Reorder the terms: (-5 + X)(X + 9) = 175 Reorder the terms: (-5 + X)(9 + X) = 175 Multiply (-5 + X) * (9 + X) (-5(9 + X) + X(9 + X)) = 175 ((9 * -5 + X * -5) + X(9 + X)) = 175 ((-45 + -5X) + X(9 + X)) = 175 (-45 + -5X + (9 * X + X * X)) = 175 (-45 + -5X + (9X + X2)) = 175 Combine like terms: -5X + 9X = 4X (-45 + 4X + X2) = 175 Solving -45 + 4X + X2 = 175 Solving for variable 'X'. Reorder the terms: -45 + -175 + 4X + X2 = 175 + -175 Combine like terms: -45 + -175 = -220 -220 + 4X + X2 = 175 + -175 Combine like terms: 175 + -175 = 0 -220 + 4X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '220' to each side of the equation. -220 + 4X + 220 + X2 = 0 + 220 Reorder the terms: -220 + 220 + 4X + X2 = 0 + 220 Combine like terms: -220 + 220 = 0 0 + 4X + X2 = 0 + 220 4X + X2 = 0 + 220 Combine like terms: 0 + 220 = 220 4X + X2 = 220 The X term is 4X. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4X + 4 + X2 = 220 + 4 Reorder the terms: 4 + 4X + X2 = 220 + 4 Combine like terms: 220 + 4 = 224 4 + 4X + X2 = 224 Factor a perfect square on the left side: (X + 2)(X + 2) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (X + 2) equal to 14.966629547 and -14.966629547.Subproblem 1
X + 2 = 14.966629547 Simplifying X + 2 = 14.966629547 Reorder the terms: 2 + X = 14.966629547 Solving 2 + X = 14.966629547 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = 14.966629547 + -2 Combine like terms: 2 + -2 = 0 0 + X = 14.966629547 + -2 X = 14.966629547 + -2 Combine like terms: 14.966629547 + -2 = 12.966629547 X = 12.966629547 Simplifying X = 12.966629547Subproblem 2
X + 2 = -14.966629547 Simplifying X + 2 = -14.966629547 Reorder the terms: 2 + X = -14.966629547 Solving 2 + X = -14.966629547 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + X = -14.966629547 + -2 Combine like terms: 2 + -2 = 0 0 + X = -14.966629547 + -2 X = -14.966629547 + -2 Combine like terms: -14.966629547 + -2 = -16.966629547 X = -16.966629547 Simplifying X = -16.966629547Solution
The solution to the problem is based on the solutions from the subproblems. X = {12.966629547, -16.966629547}
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