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Simplifying x2 + 6x + -1740 = 0 Reorder the terms: -1740 + 6x + x2 = 0 Solving -1740 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1740' to each side of the equation. -1740 + 6x + 1740 + x2 = 0 + 1740 Reorder the terms: -1740 + 1740 + 6x + x2 = 0 + 1740 Combine like terms: -1740 + 1740 = 0 0 + 6x + x2 = 0 + 1740 6x + x2 = 0 + 1740 Combine like terms: 0 + 1740 = 1740 6x + x2 = 1740 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 1740 + 9 Reorder the terms: 9 + 6x + x2 = 1740 + 9 Combine like terms: 1740 + 9 = 1749 9 + 6x + x2 = 1749 Factor a perfect square on the left side: (x + 3)(x + 3) = 1749 Calculate the square root of the right side: 41.821047333 Break this problem into two subproblems by setting (x + 3) equal to 41.821047333 and -41.821047333.Subproblem 1
x + 3 = 41.821047333 Simplifying x + 3 = 41.821047333 Reorder the terms: 3 + x = 41.821047333 Solving 3 + x = 41.821047333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 41.821047333 + -3 Combine like terms: 3 + -3 = 0 0 + x = 41.821047333 + -3 x = 41.821047333 + -3 Combine like terms: 41.821047333 + -3 = 38.821047333 x = 38.821047333 Simplifying x = 38.821047333Subproblem 2
x + 3 = -41.821047333 Simplifying x + 3 = -41.821047333 Reorder the terms: 3 + x = -41.821047333 Solving 3 + x = -41.821047333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -41.821047333 + -3 Combine like terms: 3 + -3 = 0 0 + x = -41.821047333 + -3 x = -41.821047333 + -3 Combine like terms: -41.821047333 + -3 = -44.821047333 x = -44.821047333 Simplifying x = -44.821047333Solution
The solution to the problem is based on the solutions from the subproblems. x = {38.821047333, -44.821047333}
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