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Simplifying x2 + 54x + -247 = 0 Reorder the terms: -247 + 54x + x2 = 0 Solving -247 + 54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '247' to each side of the equation. -247 + 54x + 247 + x2 = 0 + 247 Reorder the terms: -247 + 247 + 54x + x2 = 0 + 247 Combine like terms: -247 + 247 = 0 0 + 54x + x2 = 0 + 247 54x + x2 = 0 + 247 Combine like terms: 0 + 247 = 247 54x + x2 = 247 The x term is 54x. Take half its coefficient (27). Square it (729) and add it to both sides. Add '729' to each side of the equation. 54x + 729 + x2 = 247 + 729 Reorder the terms: 729 + 54x + x2 = 247 + 729 Combine like terms: 247 + 729 = 976 729 + 54x + x2 = 976 Factor a perfect square on the left side: (x + 27)(x + 27) = 976 Calculate the square root of the right side: 31.240998704 Break this problem into two subproblems by setting (x + 27) equal to 31.240998704 and -31.240998704.Subproblem 1
x + 27 = 31.240998704 Simplifying x + 27 = 31.240998704 Reorder the terms: 27 + x = 31.240998704 Solving 27 + x = 31.240998704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = 31.240998704 + -27 Combine like terms: 27 + -27 = 0 0 + x = 31.240998704 + -27 x = 31.240998704 + -27 Combine like terms: 31.240998704 + -27 = 4.240998704 x = 4.240998704 Simplifying x = 4.240998704Subproblem 2
x + 27 = -31.240998704 Simplifying x + 27 = -31.240998704 Reorder the terms: 27 + x = -31.240998704 Solving 27 + x = -31.240998704 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-27' to each side of the equation. 27 + -27 + x = -31.240998704 + -27 Combine like terms: 27 + -27 = 0 0 + x = -31.240998704 + -27 x = -31.240998704 + -27 Combine like terms: -31.240998704 + -27 = -58.240998704 x = -58.240998704 Simplifying x = -58.240998704Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.240998704, -58.240998704}
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