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Simplifying X(4X + 12) = 75 Reorder the terms: X(12 + 4X) = 75 (12 * X + 4X * X) = 75 (12X + 4X2) = 75 Solving 12X + 4X2 = 75 Solving for variable 'X'. Reorder the terms: -75 + 12X + 4X2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 12X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -18.75 + 3X + X2 = 0 Move the constant term to the right: Add '18.75' to each side of the equation. -18.75 + 3X + 18.75 + X2 = 0 + 18.75 Reorder the terms: -18.75 + 18.75 + 3X + X2 = 0 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + 3X + X2 = 0 + 18.75 3X + X2 = 0 + 18.75 Combine like terms: 0 + 18.75 = 18.75 3X + X2 = 18.75 The X term is 3X. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3X + 2.25 + X2 = 18.75 + 2.25 Reorder the terms: 2.25 + 3X + X2 = 18.75 + 2.25 Combine like terms: 18.75 + 2.25 = 21 2.25 + 3X + X2 = 21 Factor a perfect square on the left side: (X + 1.5)(X + 1.5) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (X + 1.5) equal to 4.582575695 and -4.582575695.Subproblem 1
X + 1.5 = 4.582575695 Simplifying X + 1.5 = 4.582575695 Reorder the terms: 1.5 + X = 4.582575695 Solving 1.5 + X = 4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = 4.582575695 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = 4.582575695 + -1.5 X = 4.582575695 + -1.5 Combine like terms: 4.582575695 + -1.5 = 3.082575695 X = 3.082575695 Simplifying X = 3.082575695Subproblem 2
X + 1.5 = -4.582575695 Simplifying X + 1.5 = -4.582575695 Reorder the terms: 1.5 + X = -4.582575695 Solving 1.5 + X = -4.582575695 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + X = -4.582575695 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + X = -4.582575695 + -1.5 X = -4.582575695 + -1.5 Combine like terms: -4.582575695 + -1.5 = -6.082575695 X = -6.082575695 Simplifying X = -6.082575695Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.082575695, -6.082575695}
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