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Simplifying 0 = -3x2 + 30x + -46 Reorder the terms: 0 = -46 + 30x + -3x2 Solving 0 = -46 + 30x + -3x2 Solving for variable 'x'. Combine like terms: 0 + 46 = 46 46 + -30x + 3x2 = -46 + 30x + -3x2 + 46 + -30x + 3x2 Reorder the terms: 46 + -30x + 3x2 = -46 + 46 + 30x + -30x + -3x2 + 3x2 Combine like terms: -46 + 46 = 0 46 + -30x + 3x2 = 0 + 30x + -30x + -3x2 + 3x2 46 + -30x + 3x2 = 30x + -30x + -3x2 + 3x2 Combine like terms: 30x + -30x = 0 46 + -30x + 3x2 = 0 + -3x2 + 3x2 46 + -30x + 3x2 = -3x2 + 3x2 Combine like terms: -3x2 + 3x2 = 0 46 + -30x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 15.33333333 + -10x + x2 = 0 Move the constant term to the right: Add '-15.33333333' to each side of the equation. 15.33333333 + -10x + -15.33333333 + x2 = 0 + -15.33333333 Reorder the terms: 15.33333333 + -15.33333333 + -10x + x2 = 0 + -15.33333333 Combine like terms: 15.33333333 + -15.33333333 = 0.00000000 0.00000000 + -10x + x2 = 0 + -15.33333333 -10x + x2 = 0 + -15.33333333 Combine like terms: 0 + -15.33333333 = -15.33333333 -10x + x2 = -15.33333333 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -15.33333333 + 25 Reorder the terms: 25 + -10x + x2 = -15.33333333 + 25 Combine like terms: -15.33333333 + 25 = 9.66666667 25 + -10x + x2 = 9.66666667 Factor a perfect square on the left side: (x + -5)(x + -5) = 9.66666667 Calculate the square root of the right side: 3.109126352 Break this problem into two subproblems by setting (x + -5) equal to 3.109126352 and -3.109126352.Subproblem 1
x + -5 = 3.109126352 Simplifying x + -5 = 3.109126352 Reorder the terms: -5 + x = 3.109126352 Solving -5 + x = 3.109126352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.109126352 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.109126352 + 5 x = 3.109126352 + 5 Combine like terms: 3.109126352 + 5 = 8.109126352 x = 8.109126352 Simplifying x = 8.109126352Subproblem 2
x + -5 = -3.109126352 Simplifying x + -5 = -3.109126352 Reorder the terms: -5 + x = -3.109126352 Solving -5 + x = -3.109126352 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.109126352 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.109126352 + 5 x = -3.109126352 + 5 Combine like terms: -3.109126352 + 5 = 1.890873648 x = 1.890873648 Simplifying x = 1.890873648Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.109126352, 1.890873648}
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