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Simplifying -4y2 + 36y + 1 = 0 Reorder the terms: 1 + 36y + -4y2 = 0 Solving 1 + 36y + -4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -9y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -9y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -9y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -9y + y2 = 0 + 0.25 -9y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -9y + y2 = 0.25 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 = 0.25 + 20.25 Reorder the terms: 20.25 + -9y + y2 = 0.25 + 20.25 Combine like terms: 0.25 + 20.25 = 20.5 20.25 + -9y + y2 = 20.5 Factor a perfect square on the left side: (y + -4.5)(y + -4.5) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (y + -4.5) equal to 4.527692569 and -4.527692569.Subproblem 1
y + -4.5 = 4.527692569 Simplifying y + -4.5 = 4.527692569 Reorder the terms: -4.5 + y = 4.527692569 Solving -4.5 + y = 4.527692569 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 = 4.527692569 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = 4.527692569 + 4.5 y = 4.527692569 + 4.5 Combine like terms: 4.527692569 + 4.5 = 9.027692569 y = 9.027692569 Simplifying y = 9.027692569Subproblem 2
y + -4.5 = -4.527692569 Simplifying y + -4.5 = -4.527692569 Reorder the terms: -4.5 + y = -4.527692569 Solving -4.5 + y = -4.527692569 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 = -4.527692569 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + y = -4.527692569 + 4.5 y = -4.527692569 + 4.5 Combine like terms: -4.527692569 + 4.5 = -0.027692569 y = -0.027692569 Simplifying y = -0.027692569Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.027692569, -0.027692569}
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