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Simplifying 3x2 + 168x + -1288 = 0 Reorder the terms: -1288 + 168x + 3x2 = 0 Solving -1288 + 168x + 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'. -429.3333333 + 56x + x2 = 0 Move the constant term to the right: Add '429.3333333' to each side of the equation. -429.3333333 + 56x + 429.3333333 + x2 = 0 + 429.3333333 Reorder the terms: -429.3333333 + 429.3333333 + 56x + x2 = 0 + 429.3333333 Combine like terms: -429.3333333 + 429.3333333 = 0.0000000 0.0000000 + 56x + x2 = 0 + 429.3333333 56x + x2 = 0 + 429.3333333 Combine like terms: 0 + 429.3333333 = 429.3333333 56x + x2 = 429.3333333 The x term is 56x. Take half its coefficient (28). Square it (784) and add it to both sides. Add '784' to each side of the equation. 56x + 784 + x2 = 429.3333333 + 784 Reorder the terms: 784 + 56x + x2 = 429.3333333 + 784 Combine like terms: 429.3333333 + 784 = 1213.3333333 784 + 56x + x2 = 1213.3333333 Factor a perfect square on the left side: (x + 28)(x + 28) = 1213.3333333 Calculate the square root of the right side: 34.832934606 Break this problem into two subproblems by setting (x + 28) equal to 34.832934606 and -34.832934606.Subproblem 1
x + 28 = 34.832934606 Simplifying x + 28 = 34.832934606 Reorder the terms: 28 + x = 34.832934606 Solving 28 + x = 34.832934606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = 34.832934606 + -28 Combine like terms: 28 + -28 = 0 0 + x = 34.832934606 + -28 x = 34.832934606 + -28 Combine like terms: 34.832934606 + -28 = 6.832934606 x = 6.832934606 Simplifying x = 6.832934606Subproblem 2
x + 28 = -34.832934606 Simplifying x + 28 = -34.832934606 Reorder the terms: 28 + x = -34.832934606 Solving 28 + x = -34.832934606 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-28' to each side of the equation. 28 + -28 + x = -34.832934606 + -28 Combine like terms: 28 + -28 = 0 0 + x = -34.832934606 + -28 x = -34.832934606 + -28 Combine like terms: -34.832934606 + -28 = -62.832934606 x = -62.832934606 Simplifying x = -62.832934606Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.832934606, -62.832934606}
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