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Simplifying y2 + 4y + -81 = 0 Reorder the terms: -81 + 4y + y2 = 0 Solving -81 + 4y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 4y + 81 + y2 = 0 + 81 Reorder the terms: -81 + 81 + 4y + y2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 4y + y2 = 0 + 81 4y + y2 = 0 + 81 Combine like terms: 0 + 81 = 81 4y + y2 = 81 The y term is 4y. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y + 4 + y2 = 81 + 4 Reorder the terms: 4 + 4y + y2 = 81 + 4 Combine like terms: 81 + 4 = 85 4 + 4y + y2 = 85 Factor a perfect square on the left side: (y + 2)(y + 2) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (y + 2) equal to 9.219544457 and -9.219544457.Subproblem 1
y + 2 = 9.219544457 Simplifying y + 2 = 9.219544457 Reorder the terms: 2 + y = 9.219544457 Solving 2 + y = 9.219544457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = 9.219544457 + -2 Combine like terms: 2 + -2 = 0 0 + y = 9.219544457 + -2 y = 9.219544457 + -2 Combine like terms: 9.219544457 + -2 = 7.219544457 y = 7.219544457 Simplifying y = 7.219544457Subproblem 2
y + 2 = -9.219544457 Simplifying y + 2 = -9.219544457 Reorder the terms: 2 + y = -9.219544457 Solving 2 + y = -9.219544457 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + y = -9.219544457 + -2 Combine like terms: 2 + -2 = 0 0 + y = -9.219544457 + -2 y = -9.219544457 + -2 Combine like terms: -9.219544457 + -2 = -11.219544457 y = -11.219544457 Simplifying y = -11.219544457Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.219544457, -11.219544457}
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