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Simplifying x2 + 18x + 49 = 0 Reorder the terms: 49 + 18x + x2 = 0 Solving 49 + 18x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-49' to each side of the equation. 49 + 18x + -49 + x2 = 0 + -49 Reorder the terms: 49 + -49 + 18x + x2 = 0 + -49 Combine like terms: 49 + -49 = 0 0 + 18x + x2 = 0 + -49 18x + x2 = 0 + -49 Combine like terms: 0 + -49 = -49 18x + x2 = -49 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 = -49 + 81 Reorder the terms: 81 + 18x + x2 = -49 + 81 Combine like terms: -49 + 81 = 32 81 + 18x + x2 = 32 Factor a perfect square on the left side: (x + 9)(x + 9) = 32 Calculate the square root of the right side: 5.656854249 Break this problem into two subproblems by setting (x + 9) equal to 5.656854249 and -5.656854249.Subproblem 1
x + 9 = 5.656854249 Simplifying x + 9 = 5.656854249 Reorder the terms: 9 + x = 5.656854249 Solving 9 + x = 5.656854249 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 = 5.656854249 + -9 Combine like terms: 9 + -9 = 0 0 + x = 5.656854249 + -9 x = 5.656854249 + -9 Combine like terms: 5.656854249 + -9 = -3.343145751 x = -3.343145751 Simplifying x = -3.343145751Subproblem 2
x + 9 = -5.656854249 Simplifying x + 9 = -5.656854249 Reorder the terms: 9 + x = -5.656854249 Solving 9 + x = -5.656854249 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 = -5.656854249 + -9 Combine like terms: 9 + -9 = 0 0 + x = -5.656854249 + -9 x = -5.656854249 + -9 Combine like terms: -5.656854249 + -9 = -14.656854249 x = -14.656854249 Simplifying x = -14.656854249Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.343145751, -14.656854249}
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