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Simplifying 2y2 + -56y + 52 = 0 Reorder the terms: 52 + -56y + 2y2 = 0 Solving 52 + -56y + 2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(26 + -28y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(26 + -28y + y2)' equal to zero and attempt to solve: Simplifying 26 + -28y + y2 = 0 Solving 26 + -28y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-26' to each side of the equation. 26 + -28y + -26 + y2 = 0 + -26 Reorder the terms: 26 + -26 + -28y + y2 = 0 + -26 Combine like terms: 26 + -26 = 0 0 + -28y + y2 = 0 + -26 -28y + y2 = 0 + -26 Combine like terms: 0 + -26 = -26 -28y + y2 = -26 The y term is -28y. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28y + 196 + y2 = -26 + 196 Reorder the terms: 196 + -28y + y2 = -26 + 196 Combine like terms: -26 + 196 = 170 196 + -28y + y2 = 170 Factor a perfect square on the left side: (y + -14)(y + -14) = 170 Calculate the square root of the right side: 13.03840481 Break this problem into two subproblems by setting (y + -14) equal to 13.03840481 and -13.03840481.Subproblem 1
y + -14 = 13.03840481 Simplifying y + -14 = 13.03840481 Reorder the terms: -14 + y = 13.03840481 Solving -14 + y = 13.03840481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = 13.03840481 + 14 Combine like terms: -14 + 14 = 0 0 + y = 13.03840481 + 14 y = 13.03840481 + 14 Combine like terms: 13.03840481 + 14 = 27.03840481 y = 27.03840481 Simplifying y = 27.03840481Subproblem 2
y + -14 = -13.03840481 Simplifying y + -14 = -13.03840481 Reorder the terms: -14 + y = -13.03840481 Solving -14 + y = -13.03840481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + y = -13.03840481 + 14 Combine like terms: -14 + 14 = 0 0 + y = -13.03840481 + 14 y = -13.03840481 + 14 Combine like terms: -13.03840481 + 14 = 0.96159519 y = 0.96159519 Simplifying y = 0.96159519Solution
The solution to the problem is based on the solutions from the subproblems. y = {27.03840481, 0.96159519}Solution
y = {27.03840481, 0.96159519}
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