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Simplifying x2 + 78x + 243 = 0 Reorder the terms: 243 + 78x + x2 = 0 Solving 243 + 78x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-243' to each side of the equation. 243 + 78x + -243 + x2 = 0 + -243 Reorder the terms: 243 + -243 + 78x + x2 = 0 + -243 Combine like terms: 243 + -243 = 0 0 + 78x + x2 = 0 + -243 78x + x2 = 0 + -243 Combine like terms: 0 + -243 = -243 78x + x2 = -243 The x term is 78x. Take half its coefficient (39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. 78x + 1521 + x2 = -243 + 1521 Reorder the terms: 1521 + 78x + x2 = -243 + 1521 Combine like terms: -243 + 1521 = 1278 1521 + 78x + x2 = 1278 Factor a perfect square on the left side: (x + 39)(x + 39) = 1278 Calculate the square root of the right side: 35.749125863 Break this problem into two subproblems by setting (x + 39) equal to 35.749125863 and -35.749125863.Subproblem 1
x + 39 = 35.749125863 Simplifying x + 39 = 35.749125863 Reorder the terms: 39 + x = 35.749125863 Solving 39 + x = 35.749125863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = 35.749125863 + -39 Combine like terms: 39 + -39 = 0 0 + x = 35.749125863 + -39 x = 35.749125863 + -39 Combine like terms: 35.749125863 + -39 = -3.250874137 x = -3.250874137 Simplifying x = -3.250874137Subproblem 2
x + 39 = -35.749125863 Simplifying x + 39 = -35.749125863 Reorder the terms: 39 + x = -35.749125863 Solving 39 + x = -35.749125863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-39' to each side of the equation. 39 + -39 + x = -35.749125863 + -39 Combine like terms: 39 + -39 = 0 0 + x = -35.749125863 + -39 x = -35.749125863 + -39 Combine like terms: -35.749125863 + -39 = -74.749125863 x = -74.749125863 Simplifying x = -74.749125863Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.250874137, -74.749125863}
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