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Simplifying x2 + -18x + 63 = 0 Reorder the terms: 63 + -18x + x2 = 0 Solving 63 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + -18x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + -18x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + -18x + x2 = 0 + -63 -18x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 -18x + x2 = -63 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 = -63 + 81 Reorder the terms: 81 + -18x + x2 = -63 + 81 Combine like terms: -63 + 81 = 18 81 + -18x + x2 = 18 Factor a perfect square on the left side: (x + -9)(x + -9) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (x + -9) equal to 4.242640687 and -4.242640687.Subproblem 1
x + -9 = 4.242640687 Simplifying x + -9 = 4.242640687 Reorder the terms: -9 + x = 4.242640687 Solving -9 + x = 4.242640687 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 = 4.242640687 + 9 Combine like terms: -9 + 9 = 0 0 + x = 4.242640687 + 9 x = 4.242640687 + 9 Combine like terms: 4.242640687 + 9 = 13.242640687 x = 13.242640687 Simplifying x = 13.242640687Subproblem 2
x + -9 = -4.242640687 Simplifying x + -9 = -4.242640687 Reorder the terms: -9 + x = -4.242640687 Solving -9 + x = -4.242640687 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 = -4.242640687 + 9 Combine like terms: -9 + 9 = 0 0 + x = -4.242640687 + 9 x = -4.242640687 + 9 Combine like terms: -4.242640687 + 9 = 4.757359313 x = 4.757359313 Simplifying x = 4.757359313Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.242640687, 4.757359313}
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