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Simplifying 29y2 + 3y + -72 = 0 Reorder the terms: -72 + 3y + 29y2 = 0 Solving -72 + 3y + 29y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -2.482758621 + 0.1034482759y + y2 = 0 Move the constant term to the right: Add '2.482758621' to each side of the equation. -2.482758621 + 0.1034482759y + 2.482758621 + y2 = 0 + 2.482758621 Reorder the terms: -2.482758621 + 2.482758621 + 0.1034482759y + y2 = 0 + 2.482758621 Combine like terms: -2.482758621 + 2.482758621 = 0.000000000 0.000000000 + 0.1034482759y + y2 = 0 + 2.482758621 0.1034482759y + y2 = 0 + 2.482758621 Combine like terms: 0 + 2.482758621 = 2.482758621 0.1034482759y + y2 = 2.482758621 The y term is 0.1034482759y. Take half its coefficient (0.05172413795). Square it (0.002675386447) and add it to both sides. Add '0.002675386447' to each side of the equation. 0.1034482759y + 0.002675386447 + y2 = 2.482758621 + 0.002675386447 Reorder the terms: 0.002675386447 + 0.1034482759y + y2 = 2.482758621 + 0.002675386447 Combine like terms: 2.482758621 + 0.002675386447 = 2.485434007447 0.002675386447 + 0.1034482759y + y2 = 2.485434007447 Factor a perfect square on the left side: (y + 0.05172413795)(y + 0.05172413795) = 2.485434007447 Calculate the square root of the right side: 1.57652593 Break this problem into two subproblems by setting (y + 0.05172413795) equal to 1.57652593 and -1.57652593.Subproblem 1
y + 0.05172413795 = 1.57652593 Simplifying y + 0.05172413795 = 1.57652593 Reorder the terms: 0.05172413795 + y = 1.57652593 Solving 0.05172413795 + y = 1.57652593 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.05172413795' to each side of the equation. 0.05172413795 + -0.05172413795 + y = 1.57652593 + -0.05172413795 Combine like terms: 0.05172413795 + -0.05172413795 = 0.00000000000 0.00000000000 + y = 1.57652593 + -0.05172413795 y = 1.57652593 + -0.05172413795 Combine like terms: 1.57652593 + -0.05172413795 = 1.52480179205 y = 1.52480179205 Simplifying y = 1.52480179205Subproblem 2
y + 0.05172413795 = -1.57652593 Simplifying y + 0.05172413795 = -1.57652593 Reorder the terms: 0.05172413795 + y = -1.57652593 Solving 0.05172413795 + y = -1.57652593 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.05172413795' to each side of the equation. 0.05172413795 + -0.05172413795 + y = -1.57652593 + -0.05172413795 Combine like terms: 0.05172413795 + -0.05172413795 = 0.00000000000 0.00000000000 + y = -1.57652593 + -0.05172413795 y = -1.57652593 + -0.05172413795 Combine like terms: -1.57652593 + -0.05172413795 = -1.62825006795 y = -1.62825006795 Simplifying y = -1.62825006795Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.52480179205, -1.62825006795}
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