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Simplifying y2 + -6y = 80 Reorder the terms: -6y + y2 = 80 Solving -6y + y2 = 80 Solving for variable 'y'. Reorder the terms: -80 + -6y + y2 = 80 + -80 Combine like terms: 80 + -80 = 0 -80 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -6y + 80 + y2 = 0 + 80 Reorder the terms: -80 + 80 + -6y + y2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -6y + y2 = 0 + 80 -6y + y2 = 0 + 80 Combine like terms: 0 + 80 = 80 -6y + y2 = 80 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = 80 + 9 Reorder the terms: 9 + -6y + y2 = 80 + 9 Combine like terms: 80 + 9 = 89 9 + -6y + y2 = 89 Factor a perfect square on the left side: (y + -3)(y + -3) = 89 Calculate the square root of the right side: 9.433981132 Break this problem into two subproblems by setting (y + -3) equal to 9.433981132 and -9.433981132.Subproblem 1
y + -3 = 9.433981132 Simplifying y + -3 = 9.433981132 Reorder the terms: -3 + y = 9.433981132 Solving -3 + y = 9.433981132 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = 9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + y = 9.433981132 + 3 y = 9.433981132 + 3 Combine like terms: 9.433981132 + 3 = 12.433981132 y = 12.433981132 Simplifying y = 12.433981132Subproblem 2
y + -3 = -9.433981132 Simplifying y + -3 = -9.433981132 Reorder the terms: -3 + y = -9.433981132 Solving -3 + y = -9.433981132 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + y = -9.433981132 + 3 Combine like terms: -3 + 3 = 0 0 + y = -9.433981132 + 3 y = -9.433981132 + 3 Combine like terms: -9.433981132 + 3 = -6.433981132 y = -6.433981132 Simplifying y = -6.433981132Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.433981132, -6.433981132}
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