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Simplifying x2 + -18x = 17 Reorder the terms: -18x + x2 = 17 Solving -18x + x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -18x + x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + -18x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -18x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -18x + x2 = 0 + 17 -18x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -18x + x2 = 17 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 = 17 + 81 Reorder the terms: 81 + -18x + x2 = 17 + 81 Combine like terms: 17 + 81 = 98 81 + -18x + x2 = 98 Factor a perfect square on the left side: (x + -9)(x + -9) = 98 Calculate the square root of the right side: 9.899494937 Break this problem into two subproblems by setting (x + -9) equal to 9.899494937 and -9.899494937.Subproblem 1
x + -9 = 9.899494937 Simplifying x + -9 = 9.899494937 Reorder the terms: -9 + x = 9.899494937 Solving -9 + x = 9.899494937 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 = 9.899494937 + 9 Combine like terms: -9 + 9 = 0 0 + x = 9.899494937 + 9 x = 9.899494937 + 9 Combine like terms: 9.899494937 + 9 = 18.899494937 x = 18.899494937 Simplifying x = 18.899494937Subproblem 2
x + -9 = -9.899494937 Simplifying x + -9 = -9.899494937 Reorder the terms: -9 + x = -9.899494937 Solving -9 + x = -9.899494937 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 = -9.899494937 + 9 Combine like terms: -9 + 9 = 0 0 + x = -9.899494937 + 9 x = -9.899494937 + 9 Combine like terms: -9.899494937 + 9 = -0.899494937 x = -0.899494937 Simplifying x = -0.899494937Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.899494937, -0.899494937}
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