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Simplifying x2 + -18x = -74 Reorder the terms: -18x + x2 = -74 Solving -18x + x2 = -74 Solving for variable 'x'. Reorder the terms: 74 + -18x + x2 = -74 + 74 Combine like terms: -74 + 74 = 0 74 + -18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-74' to each side of the equation. 74 + -18x + -74 + x2 = 0 + -74 Reorder the terms: 74 + -74 + -18x + x2 = 0 + -74 Combine like terms: 74 + -74 = 0 0 + -18x + x2 = 0 + -74 -18x + x2 = 0 + -74 Combine like terms: 0 + -74 = -74 -18x + x2 = -74 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 = -74 + 81 Reorder the terms: 81 + -18x + x2 = -74 + 81 Combine like terms: -74 + 81 = 7 81 + -18x + x2 = 7 Factor a perfect square on the left side: (x + -9)(x + -9) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -9) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -9 = 2.645751311 Simplifying x + -9 = 2.645751311 Reorder the terms: -9 + x = 2.645751311 Solving -9 + x = 2.645751311 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 = 2.645751311 + 9 Combine like terms: -9 + 9 = 0 0 + x = 2.645751311 + 9 x = 2.645751311 + 9 Combine like terms: 2.645751311 + 9 = 11.645751311 x = 11.645751311 Simplifying x = 11.645751311Subproblem 2
x + -9 = -2.645751311 Simplifying x + -9 = -2.645751311 Reorder the terms: -9 + x = -2.645751311 Solving -9 + x = -2.645751311 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 = -2.645751311 + 9 Combine like terms: -9 + 9 = 0 0 + x = -2.645751311 + 9 x = -2.645751311 + 9 Combine like terms: -2.645751311 + 9 = 6.354248689 x = 6.354248689 Simplifying x = 6.354248689Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.645751311, 6.354248689}
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