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Simplifying 2y2 + 15y + 21 = 0 Reorder the terms: 21 + 15y + 2y2 = 0 Solving 21 + 15y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10.5 + 7.5y + y2 = 0 Move the constant term to the right: Add '-10.5' to each side of the equation. 10.5 + 7.5y + -10.5 + y2 = 0 + -10.5 Reorder the terms: 10.5 + -10.5 + 7.5y + y2 = 0 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + 7.5y + y2 = 0 + -10.5 7.5y + y2 = 0 + -10.5 Combine like terms: 0 + -10.5 = -10.5 7.5y + y2 = -10.5 The y term is 7.5y. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5y + 14.0625 + y2 = -10.5 + 14.0625 Reorder the terms: 14.0625 + 7.5y + y2 = -10.5 + 14.0625 Combine like terms: -10.5 + 14.0625 = 3.5625 14.0625 + 7.5y + y2 = 3.5625 Factor a perfect square on the left side: (y + 3.75)(y + 3.75) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (y + 3.75) equal to 1.887458609 and -1.887458609.Subproblem 1
y + 3.75 = 1.887458609 Simplifying y + 3.75 = 1.887458609 Reorder the terms: 3.75 + y = 1.887458609 Solving 3.75 + y = 1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + y = 1.887458609 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + y = 1.887458609 + -3.75 y = 1.887458609 + -3.75 Combine like terms: 1.887458609 + -3.75 = -1.862541391 y = -1.862541391 Simplifying y = -1.862541391Subproblem 2
y + 3.75 = -1.887458609 Simplifying y + 3.75 = -1.887458609 Reorder the terms: 3.75 + y = -1.887458609 Solving 3.75 + y = -1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + y = -1.887458609 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + y = -1.887458609 + -3.75 y = -1.887458609 + -3.75 Combine like terms: -1.887458609 + -3.75 = -5.637458609 y = -5.637458609 Simplifying y = -5.637458609Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.862541391, -5.637458609}
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