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Simplifying 2X(X + 4) = 25 Reorder the terms: 2X(4 + X) = 25 (4 * 2X + X * 2X) = 25 (8X + 2X2) = 25 Solving 8X + 2X2 = 25 Solving for variable 'X'. Reorder the terms: -25 + 8X + 2X2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + 8X + 2X2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + 4X + X2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + 4X + 12.5 + X2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + 4X + X2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + 4X + X2 = 0 + 12.5 4X + X2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 4X + X2 = 12.5 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 = 12.5 + 4 Reorder the terms: 4 + 4X + X2 = 12.5 + 4 Combine like terms: 12.5 + 4 = 16.5 4 + 4X + X2 = 16.5 Factor a perfect square on the left side: (X + 2)(X + 2) = 16.5 Calculate the square root of the right side: 4.062019202 Break this problem into two subproblems by setting (X + 2) equal to 4.062019202 and -4.062019202.Subproblem 1
X + 2 = 4.062019202 Simplifying X + 2 = 4.062019202 Reorder the terms: 2 + X = 4.062019202 Solving 2 + X = 4.062019202 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 = 4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + X = 4.062019202 + -2 X = 4.062019202 + -2 Combine like terms: 4.062019202 + -2 = 2.062019202 X = 2.062019202 Simplifying X = 2.062019202Subproblem 2
X + 2 = -4.062019202 Simplifying X + 2 = -4.062019202 Reorder the terms: 2 + X = -4.062019202 Solving 2 + X = -4.062019202 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 = -4.062019202 + -2 Combine like terms: 2 + -2 = 0 0 + X = -4.062019202 + -2 X = -4.062019202 + -2 Combine like terms: -4.062019202 + -2 = -6.062019202 X = -6.062019202 Simplifying X = -6.062019202Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.062019202, -6.062019202}
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