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Simplifying 3x2 + -18x + 27 = 125 Reorder the terms: 27 + -18x + 3x2 = 125 Solving 27 + -18x + 3x2 = 125 Solving for variable 'x'. Reorder the terms: 27 + -125 + -18x + 3x2 = 125 + -125 Combine like terms: 27 + -125 = -98 -98 + -18x + 3x2 = 125 + -125 Combine like terms: 125 + -125 = 0 -98 + -18x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -32.66666667 + -6x + x2 = 0 Move the constant term to the right: Add '32.66666667' to each side of the equation. -32.66666667 + -6x + 32.66666667 + x2 = 0 + 32.66666667 Reorder the terms: -32.66666667 + 32.66666667 + -6x + x2 = 0 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + -6x + x2 = 0 + 32.66666667 -6x + x2 = 0 + 32.66666667 Combine like terms: 0 + 32.66666667 = 32.66666667 -6x + x2 = 32.66666667 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 32.66666667 + 9 Reorder the terms: 9 + -6x + x2 = 32.66666667 + 9 Combine like terms: 32.66666667 + 9 = 41.66666667 9 + -6x + x2 = 41.66666667 Factor a perfect square on the left side: (x + -3)(x + -3) = 41.66666667 Calculate the square root of the right side: 6.454972244 Break this problem into two subproblems by setting (x + -3) equal to 6.454972244 and -6.454972244.Subproblem 1
x + -3 = 6.454972244 Simplifying x + -3 = 6.454972244 Reorder the terms: -3 + x = 6.454972244 Solving -3 + x = 6.454972244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 6.454972244 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.454972244 + 3 x = 6.454972244 + 3 Combine like terms: 6.454972244 + 3 = 9.454972244 x = 9.454972244 Simplifying x = 9.454972244Subproblem 2
x + -3 = -6.454972244 Simplifying x + -3 = -6.454972244 Reorder the terms: -3 + x = -6.454972244 Solving -3 + x = -6.454972244 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -6.454972244 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.454972244 + 3 x = -6.454972244 + 3 Combine like terms: -6.454972244 + 3 = -3.454972244 x = -3.454972244 Simplifying x = -3.454972244Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.454972244, -3.454972244}
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