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Simplifying 2y2 + -20y = 43 Reorder the terms: -20y + 2y2 = 43 Solving -20y + 2y2 = 43 Solving for variable 'y'. Reorder the terms: -43 + -20y + 2y2 = 43 + -43 Combine like terms: 43 + -43 = 0 -43 + -20y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -21.5 + -10y + y2 = 0 Move the constant term to the right: Add '21.5' to each side of the equation. -21.5 + -10y + 21.5 + y2 = 0 + 21.5 Reorder the terms: -21.5 + 21.5 + -10y + y2 = 0 + 21.5 Combine like terms: -21.5 + 21.5 = 0.0 0.0 + -10y + y2 = 0 + 21.5 -10y + y2 = 0 + 21.5 Combine like terms: 0 + 21.5 = 21.5 -10y + y2 = 21.5 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = 21.5 + 25 Reorder the terms: 25 + -10y + y2 = 21.5 + 25 Combine like terms: 21.5 + 25 = 46.5 25 + -10y + y2 = 46.5 Factor a perfect square on the left side: (y + -5)(y + -5) = 46.5 Calculate the square root of the right side: 6.819090848 Break this problem into two subproblems by setting (y + -5) equal to 6.819090848 and -6.819090848.Subproblem 1
y + -5 = 6.819090848 Simplifying y + -5 = 6.819090848 Reorder the terms: -5 + y = 6.819090848 Solving -5 + y = 6.819090848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 6.819090848 + 5 Combine like terms: -5 + 5 = 0 0 + y = 6.819090848 + 5 y = 6.819090848 + 5 Combine like terms: 6.819090848 + 5 = 11.819090848 y = 11.819090848 Simplifying y = 11.819090848Subproblem 2
y + -5 = -6.819090848 Simplifying y + -5 = -6.819090848 Reorder the terms: -5 + y = -6.819090848 Solving -5 + y = -6.819090848 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -6.819090848 + 5 Combine like terms: -5 + 5 = 0 0 + y = -6.819090848 + 5 y = -6.819090848 + 5 Combine like terms: -6.819090848 + 5 = -1.819090848 y = -1.819090848 Simplifying y = -1.819090848Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.819090848, -1.819090848}
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