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Simplifying x * x + 18x = 531 Multiply x * x x2 + 18x = 531 Reorder the terms: 18x + x2 = 531 Solving 18x + x2 = 531 Solving for variable 'x'. Reorder the terms: -531 + 18x + x2 = 531 + -531 Combine like terms: 531 + -531 = 0 -531 + 18x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '531' to each side of the equation. -531 + 18x + 531 + x2 = 0 + 531 Reorder the terms: -531 + 531 + 18x + x2 = 0 + 531 Combine like terms: -531 + 531 = 0 0 + 18x + x2 = 0 + 531 18x + x2 = 0 + 531 Combine like terms: 0 + 531 = 531 18x + x2 = 531 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 = 531 + 81 Reorder the terms: 81 + 18x + x2 = 531 + 81 Combine like terms: 531 + 81 = 612 81 + 18x + x2 = 612 Factor a perfect square on the left side: (x + 9)(x + 9) = 612 Calculate the square root of the right side: 24.738633754 Break this problem into two subproblems by setting (x + 9) equal to 24.738633754 and -24.738633754.Subproblem 1
x + 9 = 24.738633754 Simplifying x + 9 = 24.738633754 Reorder the terms: 9 + x = 24.738633754 Solving 9 + x = 24.738633754 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 = 24.738633754 + -9 Combine like terms: 9 + -9 = 0 0 + x = 24.738633754 + -9 x = 24.738633754 + -9 Combine like terms: 24.738633754 + -9 = 15.738633754 x = 15.738633754 Simplifying x = 15.738633754Subproblem 2
x + 9 = -24.738633754 Simplifying x + 9 = -24.738633754 Reorder the terms: 9 + x = -24.738633754 Solving 9 + x = -24.738633754 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 = -24.738633754 + -9 Combine like terms: 9 + -9 = 0 0 + x = -24.738633754 + -9 x = -24.738633754 + -9 Combine like terms: -24.738633754 + -9 = -33.738633754 x = -33.738633754 Simplifying x = -33.738633754Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.738633754, -33.738633754}
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