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Simplifying 2y2 + -40y = 54 Reorder the terms: -40y + 2y2 = 54 Solving -40y + 2y2 = 54 Solving for variable 'y'. Reorder the terms: -54 + -40y + 2y2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -40y + 2y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -20y + y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + -20y + y2)' equal to zero and attempt to solve: Simplifying -27 + -20y + y2 = 0 Solving -27 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + -20y + 27 + y2 = 0 + 27 Reorder the terms: -27 + 27 + -20y + y2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + -20y + y2 = 0 + 27 -20y + y2 = 0 + 27 Combine like terms: 0 + 27 = 27 -20y + y2 = 27 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = 27 + 100 Reorder the terms: 100 + -20y + y2 = 27 + 100 Combine like terms: 27 + 100 = 127 100 + -20y + y2 = 127 Factor a perfect square on the left side: (y + -10)(y + -10) = 127 Calculate the square root of the right side: 11.26942767 Break this problem into two subproblems by setting (y + -10) equal to 11.26942767 and -11.26942767.Subproblem 1
y + -10 = 11.26942767 Simplifying y + -10 = 11.26942767 Reorder the terms: -10 + y = 11.26942767 Solving -10 + y = 11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + y = 11.26942767 + 10 y = 11.26942767 + 10 Combine like terms: 11.26942767 + 10 = 21.26942767 y = 21.26942767 Simplifying y = 21.26942767Subproblem 2
y + -10 = -11.26942767 Simplifying y + -10 = -11.26942767 Reorder the terms: -10 + y = -11.26942767 Solving -10 + y = -11.26942767 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -11.26942767 + 10 Combine like terms: -10 + 10 = 0 0 + y = -11.26942767 + 10 y = -11.26942767 + 10 Combine like terms: -11.26942767 + 10 = -1.26942767 y = -1.26942767 Simplifying y = -1.26942767Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.26942767, -1.26942767}Solution
y = {21.26942767, -1.26942767}
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