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Simplifying x + 1 = x2 + -25 + 25x Reorder the terms: 1 + x = x2 + -25 + 25x Reorder the terms: 1 + x = -25 + 25x + x2 Solving 1 + x = -25 + 25x + x2 Solving for variable 'x'. Reorder the terms: 1 + 25 + x + -25x + -1x2 = -25 + 25x + x2 + 25 + -25x + -1x2 Combine like terms: 1 + 25 = 26 26 + x + -25x + -1x2 = -25 + 25x + x2 + 25 + -25x + -1x2 Combine like terms: x + -25x = -24x 26 + -24x + -1x2 = -25 + 25x + x2 + 25 + -25x + -1x2 Reorder the terms: 26 + -24x + -1x2 = -25 + 25 + 25x + -25x + x2 + -1x2 Combine like terms: -25 + 25 = 0 26 + -24x + -1x2 = 0 + 25x + -25x + x2 + -1x2 26 + -24x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 26 + -24x + -1x2 = 0 + x2 + -1x2 26 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 26 + -24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -26 + 24x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + 24x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + 24x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 24x + x2 = 0 + 26 24x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 24x + x2 = 26 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 26 + 144 Reorder the terms: 144 + 24x + x2 = 26 + 144 Combine like terms: 26 + 144 = 170 144 + 24x + x2 = 170 Factor a perfect square on the left side: (x + 12)(x + 12) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + 12) equal to 13.03840481 and -13.03840481.Subproblem 1
x + 12 = 13.03840481 Simplifying x + 12 = 13.03840481 Reorder the terms: 12 + x = 13.03840481 Solving 12 + x = 13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 13.03840481 + -12 Combine like terms: 12 + -12 = 0 0 + x = 13.03840481 + -12 x = 13.03840481 + -12 Combine like terms: 13.03840481 + -12 = 1.03840481 x = 1.03840481 Simplifying x = 1.03840481Subproblem 2
x + 12 = -13.03840481 Simplifying x + 12 = -13.03840481 Reorder the terms: 12 + x = -13.03840481 Solving 12 + x = -13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -13.03840481 + -12 Combine like terms: 12 + -12 = 0 0 + x = -13.03840481 + -12 x = -13.03840481 + -12 Combine like terms: -13.03840481 + -12 = -25.03840481 x = -25.03840481 Simplifying x = -25.03840481Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.03840481, -25.03840481}
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