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Simplifying x2 + 18x = 225 Reorder the terms: 18x + x2 = 225 Solving 18x + x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 18x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 18x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 18x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 18x + x2 = 0 + 225 18x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 18x + x2 = 225 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 = 225 + 81 Reorder the terms: 81 + 18x + x2 = 225 + 81 Combine like terms: 225 + 81 = 306 81 + 18x + x2 = 306 Factor a perfect square on the left side: (x + 9)(x + 9) = 306 Calculate the square root of the right side: 17.492855685 Break this problem into two subproblems by setting (x + 9) equal to 17.492855685 and -17.492855685.Subproblem 1
x + 9 = 17.492855685 Simplifying x + 9 = 17.492855685 Reorder the terms: 9 + x = 17.492855685 Solving 9 + x = 17.492855685 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 = 17.492855685 + -9 Combine like terms: 9 + -9 = 0 0 + x = 17.492855685 + -9 x = 17.492855685 + -9 Combine like terms: 17.492855685 + -9 = 8.492855685 x = 8.492855685 Simplifying x = 8.492855685Subproblem 2
x + 9 = -17.492855685 Simplifying x + 9 = -17.492855685 Reorder the terms: 9 + x = -17.492855685 Solving 9 + x = -17.492855685 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 = -17.492855685 + -9 Combine like terms: 9 + -9 = 0 0 + x = -17.492855685 + -9 x = -17.492855685 + -9 Combine like terms: -17.492855685 + -9 = -26.492855685 x = -26.492855685 Simplifying x = -26.492855685Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.492855685, -26.492855685}
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