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Simplifying 3x2 + -132x + -548 = 0 Reorder the terms: -548 + -132x + 3x2 = 0 Solving -548 + -132x + 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'. -182.6666667 + -44x + x2 = 0 Move the constant term to the right: Add '182.6666667' to each side of the equation. -182.6666667 + -44x + 182.6666667 + x2 = 0 + 182.6666667 Reorder the terms: -182.6666667 + 182.6666667 + -44x + x2 = 0 + 182.6666667 Combine like terms: -182.6666667 + 182.6666667 = 0.0000000 0.0000000 + -44x + x2 = 0 + 182.6666667 -44x + x2 = 0 + 182.6666667 Combine like terms: 0 + 182.6666667 = 182.6666667 -44x + x2 = 182.6666667 The x term is -44x. Take half its coefficient (-22). Square it (484) and add it to both sides. Add '484' to each side of the equation. -44x + 484 + x2 = 182.6666667 + 484 Reorder the terms: 484 + -44x + x2 = 182.6666667 + 484 Combine like terms: 182.6666667 + 484 = 666.6666667 484 + -44x + x2 = 666.6666667 Factor a perfect square on the left side: (x + -22)(x + -22) = 666.6666667 Calculate the square root of the right side: 25.819888975 Break this problem into two subproblems by setting (x + -22) equal to 25.819888975 and -25.819888975.Subproblem 1
x + -22 = 25.819888975 Simplifying x + -22 = 25.819888975 Reorder the terms: -22 + x = 25.819888975 Solving -22 + x = 25.819888975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = 25.819888975 + 22 Combine like terms: -22 + 22 = 0 0 + x = 25.819888975 + 22 x = 25.819888975 + 22 Combine like terms: 25.819888975 + 22 = 47.819888975 x = 47.819888975 Simplifying x = 47.819888975Subproblem 2
x + -22 = -25.819888975 Simplifying x + -22 = -25.819888975 Reorder the terms: -22 + x = -25.819888975 Solving -22 + x = -25.819888975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22' to each side of the equation. -22 + 22 + x = -25.819888975 + 22 Combine like terms: -22 + 22 = 0 0 + x = -25.819888975 + 22 x = -25.819888975 + 22 Combine like terms: -25.819888975 + 22 = -3.819888975 x = -3.819888975 Simplifying x = -3.819888975Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.819888975, -3.819888975}
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