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Simplifying x2 + 18x = 299 Reorder the terms: 18x + x2 = 299 Solving 18x + x2 = 299 Solving for variable 'x'. Reorder the terms: -299 + 18x + x2 = 299 + -299 Combine like terms: 299 + -299 = 0 -299 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '299' to each side of the equation. -299 + 18x + 299 + x2 = 0 + 299 Reorder the terms: -299 + 299 + 18x + x2 = 0 + 299 Combine like terms: -299 + 299 = 0 0 + 18x + x2 = 0 + 299 18x + x2 = 0 + 299 Combine like terms: 0 + 299 = 299 18x + x2 = 299 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 = 299 + 81 Reorder the terms: 81 + 18x + x2 = 299 + 81 Combine like terms: 299 + 81 = 380 81 + 18x + x2 = 380 Factor a perfect square on the left side: (x + 9)(x + 9) = 380 Calculate the square root of the right side: 19.49358869 Break this problem into two subproblems by setting (x + 9) equal to 19.49358869 and -19.49358869.Subproblem 1
x + 9 = 19.49358869 Simplifying x + 9 = 19.49358869 Reorder the terms: 9 + x = 19.49358869 Solving 9 + x = 19.49358869 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 = 19.49358869 + -9 Combine like terms: 9 + -9 = 0 0 + x = 19.49358869 + -9 x = 19.49358869 + -9 Combine like terms: 19.49358869 + -9 = 10.49358869 x = 10.49358869 Simplifying x = 10.49358869Subproblem 2
x + 9 = -19.49358869 Simplifying x + 9 = -19.49358869 Reorder the terms: 9 + x = -19.49358869 Solving 9 + x = -19.49358869 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 = -19.49358869 + -9 Combine like terms: 9 + -9 = 0 0 + x = -19.49358869 + -9 x = -19.49358869 + -9 Combine like terms: -19.49358869 + -9 = -28.49358869 x = -28.49358869 Simplifying x = -28.49358869Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.49358869, -28.49358869}
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