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Simplifying 5y2 + -45y + 9 = 0 Reorder the terms: 9 + -45y + 5y2 = 0 Solving 9 + -45y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -9y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -9y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -9y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -9y + y2 = 0 + -1.8 -9y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -9y + y2 = -1.8 The y term is -9y. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9y + 20.25 + y2 = -1.8 + 20.25 Reorder the terms: 20.25 + -9y + y2 = -1.8 + 20.25 Combine like terms: -1.8 + 20.25 = 18.45 20.25 + -9y + y2 = 18.45 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 18.45 Calculate the square root of the right side: 4.295346319 Break this problem into two subproblems by setting (y + -4.5) equal to 4.295346319 and -4.295346319.Subproblem 1
y + -4.5 = 4.295346319 Simplifying y + -4.5 = 4.295346319 Reorder the terms: -4.5 + y = 4.295346319 Solving -4.5 + y = 4.295346319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = 4.295346319 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 4.295346319 + 4.5 y = 4.295346319 + 4.5 Combine like terms: 4.295346319 + 4.5 = 8.795346319 y = 8.795346319 Simplifying y = 8.795346319Subproblem 2
y + -4.5 = -4.295346319 Simplifying y + -4.5 = -4.295346319 Reorder the terms: -4.5 + y = -4.295346319 Solving -4.5 + y = -4.295346319 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + y = -4.295346319 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -4.295346319 + 4.5 y = -4.295346319 + 4.5 Combine like terms: -4.295346319 + 4.5 = 0.204653681 y = 0.204653681 Simplifying y = 0.204653681Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.795346319, 0.204653681}
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