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Simplifying x2 + 18x = 32 Reorder the terms: 18x + x2 = 32 Solving 18x + x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + 18x + x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + 18x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + 18x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + 18x + x2 = 0 + 32 18x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 18x + x2 = 32 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 = 32 + 81 Reorder the terms: 81 + 18x + x2 = 32 + 81 Combine like terms: 32 + 81 = 113 81 + 18x + x2 = 113 Factor a perfect square on the left side: (x + 9)(x + 9) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 9) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 9 = 10.630145813 Simplifying x + 9 = 10.630145813 Reorder the terms: 9 + x = 10.630145813 Solving 9 + x = 10.630145813 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 = 10.630145813 + -9 Combine like terms: 9 + -9 = 0 0 + x = 10.630145813 + -9 x = 10.630145813 + -9 Combine like terms: 10.630145813 + -9 = 1.630145813 x = 1.630145813 Simplifying x = 1.630145813Subproblem 2
x + 9 = -10.630145813 Simplifying x + 9 = -10.630145813 Reorder the terms: 9 + x = -10.630145813 Solving 9 + x = -10.630145813 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 = -10.630145813 + -9 Combine like terms: 9 + -9 = 0 0 + x = -10.630145813 + -9 x = -10.630145813 + -9 Combine like terms: -10.630145813 + -9 = -19.630145813 x = -19.630145813 Simplifying x = -19.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.630145813, -19.630145813}
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