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Simplifying 9x2 + -46x + 48 = 0 Reorder the terms: 48 + -46x + 9x2 = 0 Solving 48 + -46x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.333333333 + -5.111111111x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -5.111111111x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -5.111111111x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -5.111111111x + x2 = 0 + -5.333333333 -5.111111111x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -5.111111111x + x2 = -5.333333333 The x term is -5.111111111x. Take half its coefficient (-2.555555556). Square it (6.530864200) and add it to both sides. Add '6.530864200' to each side of the equation. -5.111111111x + 6.530864200 + x2 = -5.333333333 + 6.530864200 Reorder the terms: 6.530864200 + -5.111111111x + x2 = -5.333333333 + 6.530864200 Combine like terms: -5.333333333 + 6.530864200 = 1.197530867 6.530864200 + -5.111111111x + x2 = 1.197530867 Factor a perfect square on the left side: (x + -2.555555556)(x + -2.555555556) = 1.197530867 Calculate the square root of the right side: 1.094317535 Break this problem into two subproblems by setting (x + -2.555555556) equal to 1.094317535 and -1.094317535.Subproblem 1
x + -2.555555556 = 1.094317535 Simplifying x + -2.555555556 = 1.094317535 Reorder the terms: -2.555555556 + x = 1.094317535 Solving -2.555555556 + x = 1.094317535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + x = 1.094317535 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + x = 1.094317535 + 2.555555556 x = 1.094317535 + 2.555555556 Combine like terms: 1.094317535 + 2.555555556 = 3.649873091 x = 3.649873091 Simplifying x = 3.649873091Subproblem 2
x + -2.555555556 = -1.094317535 Simplifying x + -2.555555556 = -1.094317535 Reorder the terms: -2.555555556 + x = -1.094317535 Solving -2.555555556 + x = -1.094317535 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.555555556' to each side of the equation. -2.555555556 + 2.555555556 + x = -1.094317535 + 2.555555556 Combine like terms: -2.555555556 + 2.555555556 = 0.000000000 0.000000000 + x = -1.094317535 + 2.555555556 x = -1.094317535 + 2.555555556 Combine like terms: -1.094317535 + 2.555555556 = 1.461238021 x = 1.461238021 Simplifying x = 1.461238021Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.649873091, 1.461238021}
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