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Simplifying 5Y2 + 39Y + -72 = 0 Reorder the terms: -72 + 39Y + 5Y2 = 0 Solving -72 + 39Y + 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'. -14.4 + 7.8Y + Y2 = 0 Move the constant term to the right: Add '14.4' to each side of the equation. -14.4 + 7.8Y + 14.4 + Y2 = 0 + 14.4 Reorder the terms: -14.4 + 14.4 + 7.8Y + Y2 = 0 + 14.4 Combine like terms: -14.4 + 14.4 = 0.0 0.0 + 7.8Y + Y2 = 0 + 14.4 7.8Y + Y2 = 0 + 14.4 Combine like terms: 0 + 14.4 = 14.4 7.8Y + Y2 = 14.4 The Y term is 7.8Y. Take half its coefficient (3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. 7.8Y + 15.21 + Y2 = 14.4 + 15.21 Reorder the terms: 15.21 + 7.8Y + Y2 = 14.4 + 15.21 Combine like terms: 14.4 + 15.21 = 29.61 15.21 + 7.8Y + Y2 = 29.61 Factor a perfect square on the left side: (Y + 3.9)(Y + 3.9) = 29.61 Calculate the square root of the right side: 5.441507144 Break this problem into two subproblems by setting (Y + 3.9) equal to 5.441507144 and -5.441507144.Subproblem 1
Y + 3.9 = 5.441507144 Simplifying Y + 3.9 = 5.441507144 Reorder the terms: 3.9 + Y = 5.441507144 Solving 3.9 + Y = 5.441507144 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + Y = 5.441507144 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + Y = 5.441507144 + -3.9 Y = 5.441507144 + -3.9 Combine like terms: 5.441507144 + -3.9 = 1.541507144 Y = 1.541507144 Simplifying Y = 1.541507144Subproblem 2
Y + 3.9 = -5.441507144 Simplifying Y + 3.9 = -5.441507144 Reorder the terms: 3.9 + Y = -5.441507144 Solving 3.9 + Y = -5.441507144 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '-3.9' to each side of the equation. 3.9 + -3.9 + Y = -5.441507144 + -3.9 Combine like terms: 3.9 + -3.9 = 0.0 0.0 + Y = -5.441507144 + -3.9 Y = -5.441507144 + -3.9 Combine like terms: -5.441507144 + -3.9 = -9.341507144 Y = -9.341507144 Simplifying Y = -9.341507144Solution
The solution to the problem is based on the solutions from the subproblems. Y = {1.541507144, -9.341507144}
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