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Simplifying (x2) + 18x = 307 x2 + 18x = 307 Reorder the terms: 18x + x2 = 307 Solving 18x + x2 = 307 Solving for variable 'x'. Reorder the terms: -307 + 18x + x2 = 307 + -307 Combine like terms: 307 + -307 = 0 -307 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '307' to each side of the equation. -307 + 18x + 307 + x2 = 0 + 307 Reorder the terms: -307 + 307 + 18x + x2 = 0 + 307 Combine like terms: -307 + 307 = 0 0 + 18x + x2 = 0 + 307 18x + x2 = 0 + 307 Combine like terms: 0 + 307 = 307 18x + x2 = 307 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 = 307 + 81 Reorder the terms: 81 + 18x + x2 = 307 + 81 Combine like terms: 307 + 81 = 388 81 + 18x + x2 = 388 Factor a perfect square on the left side: (x + 9)(x + 9) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (x + 9) equal to 19.697715604 and -19.697715604.Subproblem 1
x + 9 = 19.697715604 Simplifying x + 9 = 19.697715604 Reorder the terms: 9 + x = 19.697715604 Solving 9 + x = 19.697715604 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 = 19.697715604 + -9 Combine like terms: 9 + -9 = 0 0 + x = 19.697715604 + -9 x = 19.697715604 + -9 Combine like terms: 19.697715604 + -9 = 10.697715604 x = 10.697715604 Simplifying x = 10.697715604Subproblem 2
x + 9 = -19.697715604 Simplifying x + 9 = -19.697715604 Reorder the terms: 9 + x = -19.697715604 Solving 9 + x = -19.697715604 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 = -19.697715604 + -9 Combine like terms: 9 + -9 = 0 0 + x = -19.697715604 + -9 x = -19.697715604 + -9 Combine like terms: -19.697715604 + -9 = -28.697715604 x = -28.697715604 Simplifying x = -28.697715604Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.697715604, -28.697715604}
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