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Simplifying 2y2 + 9 = -10y Reorder the terms: 9 + 2y2 = -10y Solving 9 + 2y2 = -10y Solving for variable 'y'. Reorder the terms: 9 + 10y + 2y2 = -10y + 10y Combine like terms: -10y + 10y = 0 9 + 10y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 5y + y2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 5y + -4.5 + y2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 5y + y2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 5y + y2 = 0 + -4.5 5y + y2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 5y + y2 = -4.5 The y term is 5y. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5y + 6.25 + y2 = -4.5 + 6.25 Reorder the terms: 6.25 + 5y + y2 = -4.5 + 6.25 Combine like terms: -4.5 + 6.25 = 1.75 6.25 + 5y + y2 = 1.75 Factor a perfect square on the left side: (y + 2.5)(y + 2.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (y + 2.5) equal to 1.322875656 and -1.322875656.Subproblem 1
y + 2.5 = 1.322875656 Simplifying y + 2.5 = 1.322875656 Reorder the terms: 2.5 + y = 1.322875656 Solving 2.5 + y = 1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = 1.322875656 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = 1.322875656 + -2.5 y = 1.322875656 + -2.5 Combine like terms: 1.322875656 + -2.5 = -1.177124344 y = -1.177124344 Simplifying y = -1.177124344Subproblem 2
y + 2.5 = -1.322875656 Simplifying y + 2.5 = -1.322875656 Reorder the terms: 2.5 + y = -1.322875656 Solving 2.5 + y = -1.322875656 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + y = -1.322875656 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + y = -1.322875656 + -2.5 y = -1.322875656 + -2.5 Combine like terms: -1.322875656 + -2.5 = -3.822875656 y = -3.822875656 Simplifying y = -3.822875656Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.177124344, -3.822875656}
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