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Simplifying 3X2 + -9X + -52 = 0 Reorder the terms: -52 + -9X + 3X2 = 0 Solving -52 + -9X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17.33333333 + -3X + X2 = 0 Move the constant term to the right: Add '17.33333333' to each side of the equation. -17.33333333 + -3X + 17.33333333 + X2 = 0 + 17.33333333 Reorder the terms: -17.33333333 + 17.33333333 + -3X + X2 = 0 + 17.33333333 Combine like terms: -17.33333333 + 17.33333333 = 0.00000000 0.00000000 + -3X + X2 = 0 + 17.33333333 -3X + X2 = 0 + 17.33333333 Combine like terms: 0 + 17.33333333 = 17.33333333 -3X + X2 = 17.33333333 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 = 17.33333333 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 17.33333333 + 2.25 Combine like terms: 17.33333333 + 2.25 = 19.58333333 2.25 + -3X + X2 = 19.58333333 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 19.58333333 Calculate the square root of the right side: 4.425306015 Break this problem into two subproblems by setting (X + -1.5) equal to 4.425306015 and -4.425306015.Subproblem 1
X + -1.5 = 4.425306015 Simplifying X + -1.5 = 4.425306015 Reorder the terms: -1.5 + X = 4.425306015 Solving -1.5 + X = 4.425306015 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 = 4.425306015 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 4.425306015 + 1.5 X = 4.425306015 + 1.5 Combine like terms: 4.425306015 + 1.5 = 5.925306015 X = 5.925306015 Simplifying X = 5.925306015Subproblem 2
X + -1.5 = -4.425306015 Simplifying X + -1.5 = -4.425306015 Reorder the terms: -1.5 + X = -4.425306015 Solving -1.5 + X = -4.425306015 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 = -4.425306015 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -4.425306015 + 1.5 X = -4.425306015 + 1.5 Combine like terms: -4.425306015 + 1.5 = -2.925306015 X = -2.925306015 Simplifying X = -2.925306015Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.925306015, -2.925306015}
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