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Simplifying -9 = 5y2 + -47y Reorder the terms: -9 = -47y + 5y2 Solving -9 = -47y + 5y2 Solving for variable 'y'. Reorder the terms: -9 + 47y + -5y2 = -47y + 47y + 5y2 + -5y2 Combine like terms: -47y + 47y = 0 -9 + 47y + -5y2 = 0 + 5y2 + -5y2 -9 + 47y + -5y2 = 5y2 + -5y2 Combine like terms: 5y2 + -5y2 = 0 -9 + 47y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.8 + -9.4y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -9.4y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -9.4y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -9.4y + y2 = 0 + -1.8 -9.4y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -9.4y + y2 = -1.8 The y term is -9.4y. Take half its coefficient (-4.7). Square it (22.09) and add it to both sides. Add '22.09' to each side of the equation. -9.4y + 22.09 + y2 = -1.8 + 22.09 Reorder the terms: 22.09 + -9.4y + y2 = -1.8 + 22.09 Combine like terms: -1.8 + 22.09 = 20.29 22.09 + -9.4y + y2 = 20.29 Factor a perfect square on the left side: (y + -4.7)(y + -4.7) = 20.29 Calculate the square root of the right side: 4.504442252 Break this problem into two subproblems by setting (y + -4.7) equal to 4.504442252 and -4.504442252.Subproblem 1
y + -4.7 = 4.504442252 Simplifying y + -4.7 = 4.504442252 Reorder the terms: -4.7 + y = 4.504442252 Solving -4.7 + y = 4.504442252 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + y = 4.504442252 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + y = 4.504442252 + 4.7 y = 4.504442252 + 4.7 Combine like terms: 4.504442252 + 4.7 = 9.204442252 y = 9.204442252 Simplifying y = 9.204442252Subproblem 2
y + -4.7 = -4.504442252 Simplifying y + -4.7 = -4.504442252 Reorder the terms: -4.7 + y = -4.504442252 Solving -4.7 + y = -4.504442252 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.7' to each side of the equation. -4.7 + 4.7 + y = -4.504442252 + 4.7 Combine like terms: -4.7 + 4.7 = 0.0 0.0 + y = -4.504442252 + 4.7 y = -4.504442252 + 4.7 Combine like terms: -4.504442252 + 4.7 = 0.195557748 y = 0.195557748 Simplifying y = 0.195557748Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.204442252, 0.195557748}
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