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Simplifying 3x2 + 48x + 128 = 0 Reorder the terms: 128 + 48x + 3x2 = 0 Solving 128 + 48x + 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'. 42.66666667 + 16x + x2 = 0 Move the constant term to the right: Add '-42.66666667' to each side of the equation. 42.66666667 + 16x + -42.66666667 + x2 = 0 + -42.66666667 Reorder the terms: 42.66666667 + -42.66666667 + 16x + x2 = 0 + -42.66666667 Combine like terms: 42.66666667 + -42.66666667 = 0.00000000 0.00000000 + 16x + x2 = 0 + -42.66666667 16x + x2 = 0 + -42.66666667 Combine like terms: 0 + -42.66666667 = -42.66666667 16x + x2 = -42.66666667 The x term is 16x. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16x + 64 + x2 = -42.66666667 + 64 Reorder the terms: 64 + 16x + x2 = -42.66666667 + 64 Combine like terms: -42.66666667 + 64 = 21.33333333 64 + 16x + x2 = 21.33333333 Factor a perfect square on the left side: (x + 8)(x + 8) = 21.33333333 Calculate the square root of the right side: 4.618802153 Break this problem into two subproblems by setting (x + 8) equal to 4.618802153 and -4.618802153.Subproblem 1
x + 8 = 4.618802153 Simplifying x + 8 = 4.618802153 Reorder the terms: 8 + x = 4.618802153 Solving 8 + x = 4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 4.618802153 + -8 Combine like terms: 8 + -8 = 0 0 + x = 4.618802153 + -8 x = 4.618802153 + -8 Combine like terms: 4.618802153 + -8 = -3.381197847 x = -3.381197847 Simplifying x = -3.381197847Subproblem 2
x + 8 = -4.618802153 Simplifying x + 8 = -4.618802153 Reorder the terms: 8 + x = -4.618802153 Solving 8 + x = -4.618802153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = -4.618802153 + -8 Combine like terms: 8 + -8 = 0 0 + x = -4.618802153 + -8 x = -4.618802153 + -8 Combine like terms: -4.618802153 + -8 = -12.618802153 x = -12.618802153 Simplifying x = -12.618802153Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.381197847, -12.618802153}
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