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Simplifying -1x2 + -18x + 36 = 0 Reorder the terms: 36 + -18x + -1x2 = 0 Solving 36 + -18x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 18x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 18x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 18x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 18x + x2 = 0 + 36 18x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 18x + x2 = 36 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 = 36 + 81 Reorder the terms: 81 + 18x + x2 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + 18x + x2 = 117 Factor a perfect square on the left side: (x + 9)(x + 9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + 9) equal to 10.816653826 and -10.816653826.Subproblem 1
x + 9 = 10.816653826 Simplifying x + 9 = 10.816653826 Reorder the terms: 9 + x = 10.816653826 Solving 9 + x = 10.816653826 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 = 10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.816653826 + -9 x = 10.816653826 + -9 Combine like terms: 10.816653826 + -9 = 1.816653826 x = 1.816653826 Simplifying x = 1.816653826Subproblem 2
x + 9 = -10.816653826 Simplifying x + 9 = -10.816653826 Reorder the terms: 9 + x = -10.816653826 Solving 9 + x = -10.816653826 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 = -10.816653826 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.816653826 + -9 x = -10.816653826 + -9 Combine like terms: -10.816653826 + -9 = -19.816653826 x = -19.816653826 Simplifying x = -19.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.816653826, -19.816653826}
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