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Simplifying 1612 = (5 + X) * X Reorder the terms for easier multiplication: 1612 = X(5 + X) 1612 = (5 * X + X * X) 1612 = (5X + X2) Solving 1612 = 5X + X2 Solving for variable 'X'. Reorder the terms: 1612 + -5X + -1X2 = 5X + -5X + X2 + -1X2 Combine like terms: 5X + -5X = 0 1612 + -5X + -1X2 = 0 + X2 + -1X2 1612 + -5X + -1X2 = X2 + -1X2 Combine like terms: X2 + -1X2 = 0 1612 + -5X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1612 + 5X + X2 = 0 Move the constant term to the right: Add '1612' to each side of the equation. -1612 + 5X + 1612 + X2 = 0 + 1612 Reorder the terms: -1612 + 1612 + 5X + X2 = 0 + 1612 Combine like terms: -1612 + 1612 = 0 0 + 5X + X2 = 0 + 1612 5X + X2 = 0 + 1612 Combine like terms: 0 + 1612 = 1612 5X + X2 = 1612 The X term is 5X. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5X + 6.25 + X2 = 1612 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 1612 + 6.25 Combine like terms: 1612 + 6.25 = 1618.25 6.25 + 5X + X2 = 1618.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 1618.25 Calculate the square root of the right side: 40.227478171 Break this problem into two subproblems by setting (X + 2.5) equal to 40.227478171 and -40.227478171.Subproblem 1
X + 2.5 = 40.227478171 Simplifying X + 2.5 = 40.227478171 Reorder the terms: 2.5 + X = 40.227478171 Solving 2.5 + X = 40.227478171 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = 40.227478171 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 40.227478171 + -2.5 X = 40.227478171 + -2.5 Combine like terms: 40.227478171 + -2.5 = 37.727478171 X = 37.727478171 Simplifying X = 37.727478171Subproblem 2
X + 2.5 = -40.227478171 Simplifying X + 2.5 = -40.227478171 Reorder the terms: 2.5 + X = -40.227478171 Solving 2.5 + X = -40.227478171 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + X = -40.227478171 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -40.227478171 + -2.5 X = -40.227478171 + -2.5 Combine like terms: -40.227478171 + -2.5 = -42.727478171 X = -42.727478171 Simplifying X = -42.727478171Solution
The solution to the problem is based on the solutions from the subproblems. X = {37.727478171, -42.727478171}
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