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Simplifying x2 + -18x + 11.5 = 0 Reorder the terms: 11.5 + -18x + x2 = 0 Solving 11.5 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -18x + -11.5 + x2 = 0 + -11.5 Reorder the terms: 11.5 + -11.5 + -18x + x2 = 0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -18x + x2 = 0 + -11.5 -18x + x2 = 0 + -11.5 Combine like terms: 0 + -11.5 = -11.5 -18x + x2 = -11.5 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 = -11.5 + 81 Reorder the terms: 81 + -18x + x2 = -11.5 + 81 Combine like terms: -11.5 + 81 = 69.5 81 + -18x + x2 = 69.5 Factor a perfect square on the left side: (x + -9)(x + -9) = 69.5 Calculate the square root of the right side: 8.336666 Break this problem into two subproblems by setting (x + -9) equal to 8.336666 and -8.336666.Subproblem 1
x + -9 = 8.336666 Simplifying x + -9 = 8.336666 Reorder the terms: -9 + x = 8.336666 Solving -9 + x = 8.336666 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 = 8.336666 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.336666 + 9 x = 8.336666 + 9 Combine like terms: 8.336666 + 9 = 17.336666 x = 17.336666 Simplifying x = 17.336666Subproblem 2
x + -9 = -8.336666 Simplifying x + -9 = -8.336666 Reorder the terms: -9 + x = -8.336666 Solving -9 + x = -8.336666 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 = -8.336666 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.336666 + 9 x = -8.336666 + 9 Combine like terms: -8.336666 + 9 = 0.663334 x = 0.663334 Simplifying x = 0.663334Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.336666, 0.663334}
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