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Simplifying 12x2 + -81x + -124 = 0 Reorder the terms: -124 + -81x + 12x2 = 0 Solving -124 + -81x + 12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -10.33333333 + -6.75x + x2 = 0 Move the constant term to the right: Add '10.33333333' to each side of the equation. -10.33333333 + -6.75x + 10.33333333 + x2 = 0 + 10.33333333 Reorder the terms: -10.33333333 + 10.33333333 + -6.75x + x2 = 0 + 10.33333333 Combine like terms: -10.33333333 + 10.33333333 = 0.00000000 0.00000000 + -6.75x + x2 = 0 + 10.33333333 -6.75x + x2 = 0 + 10.33333333 Combine like terms: 0 + 10.33333333 = 10.33333333 -6.75x + x2 = 10.33333333 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = 10.33333333 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = 10.33333333 + 11.390625 Combine like terms: 10.33333333 + 11.390625 = 21.72395833 11.390625 + -6.75x + x2 = 21.72395833 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 21.72395833 Calculate the square root of the right side: 4.66089673 Break this problem into two subproblems by setting (x + -3.375) equal to 4.66089673 and -4.66089673.Subproblem 1
x + -3.375 = 4.66089673 Simplifying x + -3.375 = 4.66089673 Reorder the terms: -3.375 + x = 4.66089673 Solving -3.375 + x = 4.66089673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 4.66089673 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 4.66089673 + 3.375 x = 4.66089673 + 3.375 Combine like terms: 4.66089673 + 3.375 = 8.03589673 x = 8.03589673 Simplifying x = 8.03589673Subproblem 2
x + -3.375 = -4.66089673 Simplifying x + -3.375 = -4.66089673 Reorder the terms: -3.375 + x = -4.66089673 Solving -3.375 + x = -4.66089673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -4.66089673 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -4.66089673 + 3.375 x = -4.66089673 + 3.375 Combine like terms: -4.66089673 + 3.375 = -1.28589673 x = -1.28589673 Simplifying x = -1.28589673Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.03589673, -1.28589673}
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