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Simplifying 3x2 + -18x + -58 = 0 Reorder the terms: -58 + -18x + 3x2 = 0 Solving -58 + -18x + 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'. -19.33333333 + -6x + x2 = 0 Move the constant term to the right: Add '19.33333333' to each side of the equation. -19.33333333 + -6x + 19.33333333 + x2 = 0 + 19.33333333 Reorder the terms: -19.33333333 + 19.33333333 + -6x + x2 = 0 + 19.33333333 Combine like terms: -19.33333333 + 19.33333333 = 0.00000000 0.00000000 + -6x + x2 = 0 + 19.33333333 -6x + x2 = 0 + 19.33333333 Combine like terms: 0 + 19.33333333 = 19.33333333 -6x + x2 = 19.33333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 19.33333333 + 9 Reorder the terms: 9 + -6x + x2 = 19.33333333 + 9 Combine like terms: 19.33333333 + 9 = 28.33333333 9 + -6x + x2 = 28.33333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 28.33333333 Calculate the square root of the right side: 5.322906474 Break this problem into two subproblems by setting (x + -3) equal to 5.322906474 and -5.322906474.Subproblem 1
x + -3 = 5.322906474 Simplifying x + -3 = 5.322906474 Reorder the terms: -3 + x = 5.322906474 Solving -3 + x = 5.322906474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 5.322906474 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.322906474 + 3 x = 5.322906474 + 3 Combine like terms: 5.322906474 + 3 = 8.322906474 x = 8.322906474 Simplifying x = 8.322906474Subproblem 2
x + -3 = -5.322906474 Simplifying x + -3 = -5.322906474 Reorder the terms: -3 + x = -5.322906474 Solving -3 + x = -5.322906474 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -5.322906474 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.322906474 + 3 x = -5.322906474 + 3 Combine like terms: -5.322906474 + 3 = -2.322906474 x = -2.322906474 Simplifying x = -2.322906474Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.322906474, -2.322906474}
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