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Simplifying x2 + -54x + 25 = 0 Reorder the terms: 25 + -54x + x2 = 0 Solving 25 + -54x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -54x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -54x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -54x + x2 = 0 + -25 -54x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -54x + x2 = -25 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 = -25 + 729 Reorder the terms: 729 + -54x + x2 = -25 + 729 Combine like terms: -25 + 729 = 704 729 + -54x + x2 = 704 Factor a perfect square on the left side: (x + -27)(x + -27) = 704 Calculate the square root of the right side: 26.532998323 Break this problem into two subproblems by setting (x + -27) equal to 26.532998323 and -26.532998323.Subproblem 1
x + -27 = 26.532998323 Simplifying x + -27 = 26.532998323 Reorder the terms: -27 + x = 26.532998323 Solving -27 + x = 26.532998323 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 = 26.532998323 + 27 Combine like terms: -27 + 27 = 0 0 + x = 26.532998323 + 27 x = 26.532998323 + 27 Combine like terms: 26.532998323 + 27 = 53.532998323 x = 53.532998323 Simplifying x = 53.532998323Subproblem 2
x + -27 = -26.532998323 Simplifying x + -27 = -26.532998323 Reorder the terms: -27 + x = -26.532998323 Solving -27 + x = -26.532998323 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 = -26.532998323 + 27 Combine like terms: -27 + 27 = 0 0 + x = -26.532998323 + 27 x = -26.532998323 + 27 Combine like terms: -26.532998323 + 27 = 0.467001677 x = 0.467001677 Simplifying x = 0.467001677Solution
The solution to the problem is based on the solutions from the subproblems. x = {53.532998323, 0.467001677}
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