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Simplifying x2 + -28x + 98 = 72 Reorder the terms: 98 + -28x + x2 = 72 Solving 98 + -28x + x2 = 72 Solving for variable 'x'. Reorder the terms: 98 + -72 + -28x + x2 = 72 + -72 Combine like terms: 98 + -72 = 26 26 + -28x + x2 = 72 + -72 Combine like terms: 72 + -72 = 0 26 + -28x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -28x + -26 + x2 = 0 + -26 Reorder the terms: 26 + -26 + -28x + x2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -28x + x2 = 0 + -26 -28x + x2 = 0 + -26 Combine like terms: 0 + -26 = -26 -28x + x2 = -26 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -26 + 196 Reorder the terms: 196 + -28x + x2 = -26 + 196 Combine like terms: -26 + 196 = 170 196 + -28x + x2 = 170 Factor a perfect square on the left side: (x + -14)(x + -14) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (x + -14) equal to 13.03840481 and -13.03840481.Subproblem 1
x + -14 = 13.03840481 Simplifying x + -14 = 13.03840481 Reorder the terms: -14 + x = 13.03840481 Solving -14 + x = 13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 13.03840481 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.03840481 + 14 x = 13.03840481 + 14 Combine like terms: 13.03840481 + 14 = 27.03840481 x = 27.03840481 Simplifying x = 27.03840481Subproblem 2
x + -14 = -13.03840481 Simplifying x + -14 = -13.03840481 Reorder the terms: -14 + x = -13.03840481 Solving -14 + x = -13.03840481 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -13.03840481 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.03840481 + 14 x = -13.03840481 + 14 Combine like terms: -13.03840481 + 14 = 0.96159519 x = 0.96159519 Simplifying x = 0.96159519Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.03840481, 0.96159519}
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