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Simplifying x2 + 18x = 385 Reorder the terms: 18x + x2 = 385 Solving 18x + x2 = 385 Solving for variable 'x'. Reorder the terms: -385 + 18x + x2 = 385 + -385 Combine like terms: 385 + -385 = 0 -385 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '385' to each side of the equation. -385 + 18x + 385 + x2 = 0 + 385 Reorder the terms: -385 + 385 + 18x + x2 = 0 + 385 Combine like terms: -385 + 385 = 0 0 + 18x + x2 = 0 + 385 18x + x2 = 0 + 385 Combine like terms: 0 + 385 = 385 18x + x2 = 385 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 = 385 + 81 Reorder the terms: 81 + 18x + x2 = 385 + 81 Combine like terms: 385 + 81 = 466 81 + 18x + x2 = 466 Factor a perfect square on the left side: (x + 9)(x + 9) = 466 Calculate the square root of the right side: 21.587033145 Break this problem into two subproblems by setting (x + 9) equal to 21.587033145 and -21.587033145.Subproblem 1
x + 9 = 21.587033145 Simplifying x + 9 = 21.587033145 Reorder the terms: 9 + x = 21.587033145 Solving 9 + x = 21.587033145 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 = 21.587033145 + -9 Combine like terms: 9 + -9 = 0 0 + x = 21.587033145 + -9 x = 21.587033145 + -9 Combine like terms: 21.587033145 + -9 = 12.587033145 x = 12.587033145 Simplifying x = 12.587033145Subproblem 2
x + 9 = -21.587033145 Simplifying x + 9 = -21.587033145 Reorder the terms: 9 + x = -21.587033145 Solving 9 + x = -21.587033145 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 = -21.587033145 + -9 Combine like terms: 9 + -9 = 0 0 + x = -21.587033145 + -9 x = -21.587033145 + -9 Combine like terms: -21.587033145 + -9 = -30.587033145 x = -30.587033145 Simplifying x = -30.587033145Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.587033145, -30.587033145}
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