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Simplifying -2y2 + 16y + 9 = 0 Reorder the terms: 9 + 16y + -2y2 = 0 Solving 9 + 16y + -2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -4.5 + -8y + y2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -8y + 4.5 + y2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -8y + y2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -8y + y2 = 0 + 4.5 -8y + y2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -8y + y2 = 4.5 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 4.5 + 16 Reorder the terms: 16 + -8y + y2 = 4.5 + 16 Combine like terms: 4.5 + 16 = 20.5 16 + -8y + y2 = 20.5 Factor a perfect square on the left side: (y + -4)(y + -4) = 20.5 Calculate the square root of the right side: 4.527692569 Break this problem into two subproblems by setting (y + -4) equal to 4.527692569 and -4.527692569.Subproblem 1
y + -4 = 4.527692569 Simplifying y + -4 = 4.527692569 Reorder the terms: -4 + y = 4.527692569 Solving -4 + y = 4.527692569 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + y = 4.527692569 + 4 y = 4.527692569 + 4 Combine like terms: 4.527692569 + 4 = 8.527692569 y = 8.527692569 Simplifying y = 8.527692569Subproblem 2
y + -4 = -4.527692569 Simplifying y + -4 = -4.527692569 Reorder the terms: -4 + y = -4.527692569 Solving -4 + y = -4.527692569 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -4.527692569 + 4 Combine like terms: -4 + 4 = 0 0 + y = -4.527692569 + 4 y = -4.527692569 + 4 Combine like terms: -4.527692569 + 4 = -0.527692569 y = -0.527692569 Simplifying y = -0.527692569Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.527692569, -0.527692569}
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