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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 = 2.925306015 x = 2.925306015 Simplifying x = 2.925306015Subproblem 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 = -5.925306015 x = -5.925306015 Simplifying x = -5.925306015Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.925306015, -5.925306015}
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