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Simplifying x2 + -18x + -65 = 0 Reorder the terms: -65 + -18x + x2 = 0 Solving -65 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '65' to each side of the equation. -65 + -18x + 65 + x2 = 0 + 65 Reorder the terms: -65 + 65 + -18x + x2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + -18x + x2 = 0 + 65 -18x + x2 = 0 + 65 Combine like terms: 0 + 65 = 65 -18x + x2 = 65 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 = 65 + 81 Reorder the terms: 81 + -18x + x2 = 65 + 81 Combine like terms: 65 + 81 = 146 81 + -18x + x2 = 146 Factor a perfect square on the left side: (x + -9)(x + -9) = 146 Calculate the square root of the right side: 12.083045974 Break this problem into two subproblems by setting (x + -9) equal to 12.083045974 and -12.083045974.Subproblem 1
x + -9 = 12.083045974 Simplifying x + -9 = 12.083045974 Reorder the terms: -9 + x = 12.083045974 Solving -9 + x = 12.083045974 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 = 12.083045974 + 9 Combine like terms: -9 + 9 = 0 0 + x = 12.083045974 + 9 x = 12.083045974 + 9 Combine like terms: 12.083045974 + 9 = 21.083045974 x = 21.083045974 Simplifying x = 21.083045974Subproblem 2
x + -9 = -12.083045974 Simplifying x + -9 = -12.083045974 Reorder the terms: -9 + x = -12.083045974 Solving -9 + x = -12.083045974 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 = -12.083045974 + 9 Combine like terms: -9 + 9 = 0 0 + x = -12.083045974 + 9 x = -12.083045974 + 9 Combine like terms: -12.083045974 + 9 = -3.083045974 x = -3.083045974 Simplifying x = -3.083045974Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.083045974, -3.083045974}
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