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Simplifying 9x2 + 46x + -70 = 0 Reorder the terms: -70 + 46x + 9x2 = 0 Solving -70 + 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'. -7.777777778 + 5.111111111x + x2 = 0 Move the constant term to the right: Add '7.777777778' to each side of the equation. -7.777777778 + 5.111111111x + 7.777777778 + x2 = 0 + 7.777777778 Reorder the terms: -7.777777778 + 7.777777778 + 5.111111111x + x2 = 0 + 7.777777778 Combine like terms: -7.777777778 + 7.777777778 = 0.000000000 0.000000000 + 5.111111111x + x2 = 0 + 7.777777778 5.111111111x + x2 = 0 + 7.777777778 Combine like terms: 0 + 7.777777778 = 7.777777778 5.111111111x + x2 = 7.777777778 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 = 7.777777778 + 6.530864200 Reorder the terms: 6.530864200 + 5.111111111x + x2 = 7.777777778 + 6.530864200 Combine like terms: 7.777777778 + 6.530864200 = 14.308641978 6.530864200 + 5.111111111x + x2 = 14.308641978 Factor a perfect square on the left side: (x + 2.555555556)(x + 2.555555556) = 14.308641978 Calculate the square root of the right side: 3.782676563 Break this problem into two subproblems by setting (x + 2.555555556) equal to 3.782676563 and -3.782676563.Subproblem 1
x + 2.555555556 = 3.782676563 Simplifying x + 2.555555556 = 3.782676563 Reorder the terms: 2.555555556 + x = 3.782676563 Solving 2.555555556 + x = 3.782676563 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 = 3.782676563 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = 3.782676563 + -2.555555556 x = 3.782676563 + -2.555555556 Combine like terms: 3.782676563 + -2.555555556 = 1.227121007 x = 1.227121007 Simplifying x = 1.227121007Subproblem 2
x + 2.555555556 = -3.782676563 Simplifying x + 2.555555556 = -3.782676563 Reorder the terms: 2.555555556 + x = -3.782676563 Solving 2.555555556 + x = -3.782676563 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 = -3.782676563 + -2.555555556 Combine like terms: 2.555555556 + -2.555555556 = 0.000000000 0.000000000 + x = -3.782676563 + -2.555555556 x = -3.782676563 + -2.555555556 Combine like terms: -3.782676563 + -2.555555556 = -6.338232119 x = -6.338232119 Simplifying x = -6.338232119Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.227121007, -6.338232119}
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