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Simplifying 3 + -4X(2 + -1X) = 7X(X + 1) 3 + (2 * -4X + -1X * -4X) = 7X(X + 1) 3 + (-8X + 4X2) = 7X(X + 1) Reorder the terms: 3 + -8X + 4X2 = 7X(1 + X) 3 + -8X + 4X2 = (1 * 7X + X * 7X) 3 + -8X + 4X2 = (7X + 7X2) Solving 3 + -8X + 4X2 = 7X + 7X2 Solving for variable 'X'. Reorder the terms: 3 + -8X + -7X + 4X2 + -7X2 = 7X + 7X2 + -7X + -7X2 Combine like terms: -8X + -7X = -15X 3 + -15X + 4X2 + -7X2 = 7X + 7X2 + -7X + -7X2 Combine like terms: 4X2 + -7X2 = -3X2 3 + -15X + -3X2 = 7X + 7X2 + -7X + -7X2 Reorder the terms: 3 + -15X + -3X2 = 7X + -7X + 7X2 + -7X2 Combine like terms: 7X + -7X = 0 3 + -15X + -3X2 = 0 + 7X2 + -7X2 3 + -15X + -3X2 = 7X2 + -7X2 Combine like terms: 7X2 + -7X2 = 0 3 + -15X + -3X2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -5X + -1X2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -5X + -1X2)' equal to zero and attempt to solve: Simplifying 1 + -5X + -1X2 = 0 Solving 1 + -5X + -1X2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1 + 5X + X2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 5X + 1 + X2 = 0 + 1 Reorder the terms: -1 + 1 + 5X + X2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 5X + X2 = 0 + 1 5X + X2 = 0 + 1 Combine like terms: 0 + 1 = 1 5X + X2 = 1 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 = 1 + 6.25 Reorder the terms: 6.25 + 5X + X2 = 1 + 6.25 Combine like terms: 1 + 6.25 = 7.25 6.25 + 5X + X2 = 7.25 Factor a perfect square on the left side: (X + 2.5)(X + 2.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (X + 2.5) equal to 2.692582404 and -2.692582404.Subproblem 1
X + 2.5 = 2.692582404 Simplifying X + 2.5 = 2.692582404 Reorder the terms: 2.5 + X = 2.692582404 Solving 2.5 + X = 2.692582404 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 = 2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = 2.692582404 + -2.5 X = 2.692582404 + -2.5 Combine like terms: 2.692582404 + -2.5 = 0.192582404 X = 0.192582404 Simplifying X = 0.192582404Subproblem 2
X + 2.5 = -2.692582404 Simplifying X + 2.5 = -2.692582404 Reorder the terms: 2.5 + X = -2.692582404 Solving 2.5 + X = -2.692582404 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 = -2.692582404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + X = -2.692582404 + -2.5 X = -2.692582404 + -2.5 Combine like terms: -2.692582404 + -2.5 = -5.192582404 X = -5.192582404 Simplifying X = -5.192582404Solution
The solution to the problem is based on the solutions from the subproblems. X = {0.192582404, -5.192582404}Solution
X = {0.192582404, -5.192582404}
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