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Simplifying 12x2 + -216x + 665 = 0 Reorder the terms: 665 + -216x + 12x2 = 0 Solving 665 + -216x + 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'. 55.41666667 + -18x + x2 = 0 Move the constant term to the right: Add '-55.41666667' to each side of the equation. 55.41666667 + -18x + -55.41666667 + x2 = 0 + -55.41666667 Reorder the terms: 55.41666667 + -55.41666667 + -18x + x2 = 0 + -55.41666667 Combine like terms: 55.41666667 + -55.41666667 = 0.00000000 0.00000000 + -18x + x2 = 0 + -55.41666667 -18x + x2 = 0 + -55.41666667 Combine like terms: 0 + -55.41666667 = -55.41666667 -18x + x2 = -55.41666667 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = -55.41666667 + 81 Reorder the terms: 81 + -18x + x2 = -55.41666667 + 81 Combine like terms: -55.41666667 + 81 = 25.58333333 81 + -18x + x2 = 25.58333333 Factor a perfect square on the left side: (x + -9)(x + -9) = 25.58333333 Calculate the square root of the right side: 5.057996968 Break this problem into two subproblems by setting (x + -9) equal to 5.057996968 and -5.057996968.Subproblem 1
x + -9 = 5.057996968 Simplifying x + -9 = 5.057996968 Reorder the terms: -9 + x = 5.057996968 Solving -9 + x = 5.057996968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 5.057996968 + 9 Combine like terms: -9 + 9 = 0 0 + x = 5.057996968 + 9 x = 5.057996968 + 9 Combine like terms: 5.057996968 + 9 = 14.057996968 x = 14.057996968 Simplifying x = 14.057996968Subproblem 2
x + -9 = -5.057996968 Simplifying x + -9 = -5.057996968 Reorder the terms: -9 + x = -5.057996968 Solving -9 + x = -5.057996968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -5.057996968 + 9 Combine like terms: -9 + 9 = 0 0 + x = -5.057996968 + 9 x = -5.057996968 + 9 Combine like terms: -5.057996968 + 9 = 3.942003032 x = 3.942003032 Simplifying x = 3.942003032Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.057996968, 3.942003032}
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