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Simplifying 5y2 + -40y + 44 = 0 Reorder the terms: 44 + -40y + 5y2 = 0 Solving 44 + -40y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 8.8 + -8y + y2 = 0 Move the constant term to the right: Add '-8.8' to each side of the equation. 8.8 + -8y + -8.8 + y2 = 0 + -8.8 Reorder the terms: 8.8 + -8.8 + -8y + y2 = 0 + -8.8 Combine like terms: 8.8 + -8.8 = 0.0 0.0 + -8y + y2 = 0 + -8.8 -8y + y2 = 0 + -8.8 Combine like terms: 0 + -8.8 = -8.8 -8y + y2 = -8.8 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -8.8 + 16 Reorder the terms: 16 + -8y + y2 = -8.8 + 16 Combine like terms: -8.8 + 16 = 7.2 16 + -8y + y2 = 7.2 Factor a perfect square on the left side: (y + -4)(y + -4) = 7.2 Calculate the square root of the right side: 2.683281573 Break this problem into two subproblems by setting (y + -4) equal to 2.683281573 and -2.683281573.Subproblem 1
y + -4 = 2.683281573 Simplifying y + -4 = 2.683281573 Reorder the terms: -4 + y = 2.683281573 Solving -4 + y = 2.683281573 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 2.683281573 + 4 Combine like terms: -4 + 4 = 0 0 + y = 2.683281573 + 4 y = 2.683281573 + 4 Combine like terms: 2.683281573 + 4 = 6.683281573 y = 6.683281573 Simplifying y = 6.683281573Subproblem 2
y + -4 = -2.683281573 Simplifying y + -4 = -2.683281573 Reorder the terms: -4 + y = -2.683281573 Solving -4 + y = -2.683281573 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -2.683281573 + 4 Combine like terms: -4 + 4 = 0 0 + y = -2.683281573 + 4 y = -2.683281573 + 4 Combine like terms: -2.683281573 + 4 = 1.316718427 y = 1.316718427 Simplifying y = 1.316718427Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.683281573, 1.316718427}
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