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Simplifying 9x2 + 64x + 48 = 0 Reorder the terms: 48 + 64x + 9x2 = 0 Solving 48 + 64x + 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 + 7.111111111x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 7.111111111x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 7.111111111x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 7.111111111x + x2 = 0 + -5.333333333 7.111111111x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 7.111111111x + x2 = -5.333333333 The x term is 7.111111111x. Take half its coefficient (3.555555556). Square it (12.64197531) and add it to both sides. Add '12.64197531' to each side of the equation. 7.111111111x + 12.64197531 + x2 = -5.333333333 + 12.64197531 Reorder the terms: 12.64197531 + 7.111111111x + x2 = -5.333333333 + 12.64197531 Combine like terms: -5.333333333 + 12.64197531 = 7.308641977 12.64197531 + 7.111111111x + x2 = 7.308641977 Factor a perfect square on the left side: (x + 3.555555556)(x + 3.555555556) = 7.308641977 Calculate the square root of the right side: 2.703450014 Break this problem into two subproblems by setting (x + 3.555555556) equal to 2.703450014 and -2.703450014.Subproblem 1
x + 3.555555556 = 2.703450014 Simplifying x + 3.555555556 = 2.703450014 Reorder the terms: 3.555555556 + x = 2.703450014 Solving 3.555555556 + x = 2.703450014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.555555556' to each side of the equation. 3.555555556 + -3.555555556 + x = 2.703450014 + -3.555555556 Combine like terms: 3.555555556 + -3.555555556 = 0.000000000 0.000000000 + x = 2.703450014 + -3.555555556 x = 2.703450014 + -3.555555556 Combine like terms: 2.703450014 + -3.555555556 = -0.852105542 x = -0.852105542 Simplifying x = -0.852105542Subproblem 2
x + 3.555555556 = -2.703450014 Simplifying x + 3.555555556 = -2.703450014 Reorder the terms: 3.555555556 + x = -2.703450014 Solving 3.555555556 + x = -2.703450014 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.555555556' to each side of the equation. 3.555555556 + -3.555555556 + x = -2.703450014 + -3.555555556 Combine like terms: 3.555555556 + -3.555555556 = 0.000000000 0.000000000 + x = -2.703450014 + -3.555555556 x = -2.703450014 + -3.555555556 Combine like terms: -2.703450014 + -3.555555556 = -6.25900557 x = -6.25900557 Simplifying x = -6.25900557Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.852105542, -6.25900557}
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