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Simplifying 3x2 + 9x + -247 = 0 Reorder the terms: -247 + 9x + 3x2 = 0 Solving -247 + 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'. -82.33333333 + 3x + x2 = 0 Move the constant term to the right: Add '82.33333333' to each side of the equation. -82.33333333 + 3x + 82.33333333 + x2 = 0 + 82.33333333 Reorder the terms: -82.33333333 + 82.33333333 + 3x + x2 = 0 + 82.33333333 Combine like terms: -82.33333333 + 82.33333333 = 0.00000000 0.00000000 + 3x + x2 = 0 + 82.33333333 3x + x2 = 0 + 82.33333333 Combine like terms: 0 + 82.33333333 = 82.33333333 3x + x2 = 82.33333333 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 = 82.33333333 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 82.33333333 + 2.25 Combine like terms: 82.33333333 + 2.25 = 84.58333333 2.25 + 3x + x2 = 84.58333333 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 84.58333333 Calculate the square root of the right side: 9.196919774 Break this problem into two subproblems by setting (x + 1.5) equal to 9.196919774 and -9.196919774.Subproblem 1
x + 1.5 = 9.196919774 Simplifying x + 1.5 = 9.196919774 Reorder the terms: 1.5 + x = 9.196919774 Solving 1.5 + x = 9.196919774 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 = 9.196919774 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 9.196919774 + -1.5 x = 9.196919774 + -1.5 Combine like terms: 9.196919774 + -1.5 = 7.696919774 x = 7.696919774 Simplifying x = 7.696919774Subproblem 2
x + 1.5 = -9.196919774 Simplifying x + 1.5 = -9.196919774 Reorder the terms: 1.5 + x = -9.196919774 Solving 1.5 + x = -9.196919774 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 = -9.196919774 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -9.196919774 + -1.5 x = -9.196919774 + -1.5 Combine like terms: -9.196919774 + -1.5 = -10.696919774 x = -10.696919774 Simplifying x = -10.696919774Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.696919774, -10.696919774}
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