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Simplifying 9y2 + -4y = 10 Reorder the terms: -4y + 9y2 = 10 Solving -4y + 9y2 = 10 Solving for variable 'y'. Reorder the terms: -10 + -4y + 9y2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + -4y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.111111111 + -0.4444444444y + y2 = 0 Move the constant term to the right: Add '1.111111111' to each side of the equation. -1.111111111 + -0.4444444444y + 1.111111111 + y2 = 0 + 1.111111111 Reorder the terms: -1.111111111 + 1.111111111 + -0.4444444444y + y2 = 0 + 1.111111111 Combine like terms: -1.111111111 + 1.111111111 = 0.000000000 0.000000000 + -0.4444444444y + y2 = 0 + 1.111111111 -0.4444444444y + y2 = 0 + 1.111111111 Combine like terms: 0 + 1.111111111 = 1.111111111 -0.4444444444y + y2 = 1.111111111 The y term is -0.4444444444y. Take half its coefficient (-0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. -0.4444444444y + 0.04938271604 + y2 = 1.111111111 + 0.04938271604 Reorder the terms: 0.04938271604 + -0.4444444444y + y2 = 1.111111111 + 0.04938271604 Combine like terms: 1.111111111 + 0.04938271604 = 1.16049382704 0.04938271604 + -0.4444444444y + y2 = 1.16049382704 Factor a perfect square on the left side: (y + -0.2222222222)(y + -0.2222222222) = 1.16049382704 Calculate the square root of the right side: 1.07726219 Break this problem into two subproblems by setting (y + -0.2222222222) equal to 1.07726219 and -1.07726219.Subproblem 1
y + -0.2222222222 = 1.07726219 Simplifying y + -0.2222222222 = 1.07726219 Reorder the terms: -0.2222222222 + y = 1.07726219 Solving -0.2222222222 + y = 1.07726219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + y = 1.07726219 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + y = 1.07726219 + 0.2222222222 y = 1.07726219 + 0.2222222222 Combine like terms: 1.07726219 + 0.2222222222 = 1.2994844122 y = 1.2994844122 Simplifying y = 1.2994844122Subproblem 2
y + -0.2222222222 = -1.07726219 Simplifying y + -0.2222222222 = -1.07726219 Reorder the terms: -0.2222222222 + y = -1.07726219 Solving -0.2222222222 + y = -1.07726219 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2222222222' to each side of the equation. -0.2222222222 + 0.2222222222 + y = -1.07726219 + 0.2222222222 Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000 0.0000000000 + y = -1.07726219 + 0.2222222222 y = -1.07726219 + 0.2222222222 Combine like terms: -1.07726219 + 0.2222222222 = -0.8550399678 y = -0.8550399678 Simplifying y = -0.8550399678Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.2994844122, -0.8550399678}
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