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Simplifying (x2) + -1(18x) + 14 = 0 x2 + -1(18x) + 14 = 0 Remove parenthesis around (18x) x2 + -1 * 18x + 14 = 0 Multiply -1 * 18 x2 + -18x + 14 = 0 Reorder the terms: 14 + -18x + x2 = 0 Solving 14 + -18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -18x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -18x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -18x + x2 = 0 + -14 -18x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -18x + x2 = -14 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 = -14 + 81 Reorder the terms: 81 + -18x + x2 = -14 + 81 Combine like terms: -14 + 81 = 67 81 + -18x + x2 = 67 Factor a perfect square on the left side: (x + -9)(x + -9) = 67 Calculate the square root of the right side: 8.185352772 Break this problem into two subproblems by setting (x + -9) equal to 8.185352772 and -8.185352772.Subproblem 1
x + -9 = 8.185352772 Simplifying x + -9 = 8.185352772 Reorder the terms: -9 + x = 8.185352772 Solving -9 + x = 8.185352772 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 = 8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + x = 8.185352772 + 9 x = 8.185352772 + 9 Combine like terms: 8.185352772 + 9 = 17.185352772 x = 17.185352772 Simplifying x = 17.185352772Subproblem 2
x + -9 = -8.185352772 Simplifying x + -9 = -8.185352772 Reorder the terms: -9 + x = -8.185352772 Solving -9 + x = -8.185352772 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 = -8.185352772 + 9 Combine like terms: -9 + 9 = 0 0 + x = -8.185352772 + 9 x = -8.185352772 + 9 Combine like terms: -8.185352772 + 9 = 0.814647228 x = 0.814647228 Simplifying x = 0.814647228Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.185352772, 0.814647228}
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