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Simplifying 6x2 + 57x + 56 = 0 Reorder the terms: 56 + 57x + 6x2 = 0 Solving 56 + 57x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 9.333333333 + 9.5x + x2 = 0 Move the constant term to the right: Add '-9.333333333' to each side of the equation. 9.333333333 + 9.5x + -9.333333333 + x2 = 0 + -9.333333333 Reorder the terms: 9.333333333 + -9.333333333 + 9.5x + x2 = 0 + -9.333333333 Combine like terms: 9.333333333 + -9.333333333 = 0.000000000 0.000000000 + 9.5x + x2 = 0 + -9.333333333 9.5x + x2 = 0 + -9.333333333 Combine like terms: 0 + -9.333333333 = -9.333333333 9.5x + x2 = -9.333333333 The x term is 9.5x. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5x + 22.5625 + x2 = -9.333333333 + 22.5625 Reorder the terms: 22.5625 + 9.5x + x2 = -9.333333333 + 22.5625 Combine like terms: -9.333333333 + 22.5625 = 13.229166667 22.5625 + 9.5x + x2 = 13.229166667 Factor a perfect square on the left side: (x + 4.75)(x + 4.75) = 13.229166667 Calculate the square root of the right side: 3.637192141 Break this problem into two subproblems by setting (x + 4.75) equal to 3.637192141 and -3.637192141.Subproblem 1
x + 4.75 = 3.637192141 Simplifying x + 4.75 = 3.637192141 Reorder the terms: 4.75 + x = 3.637192141 Solving 4.75 + x = 3.637192141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = 3.637192141 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = 3.637192141 + -4.75 x = 3.637192141 + -4.75 Combine like terms: 3.637192141 + -4.75 = -1.112807859 x = -1.112807859 Simplifying x = -1.112807859Subproblem 2
x + 4.75 = -3.637192141 Simplifying x + 4.75 = -3.637192141 Reorder the terms: 4.75 + x = -3.637192141 Solving 4.75 + x = -3.637192141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + x = -3.637192141 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + x = -3.637192141 + -4.75 x = -3.637192141 + -4.75 Combine like terms: -3.637192141 + -4.75 = -8.387192141 x = -8.387192141 Simplifying x = -8.387192141Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.112807859, -8.387192141}
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