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Simplifying y2 + -6y + 2 = 81 Reorder the terms: 2 + -6y + y2 = 81 Solving 2 + -6y + y2 = 81 Solving for variable 'y'. Reorder the terms: 2 + -81 + -6y + y2 = 81 + -81 Combine like terms: 2 + -81 = -79 -79 + -6y + y2 = 81 + -81 Combine like terms: 81 + -81 = 0 -79 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '79' to each side of the equation. -79 + -6y + 79 + y2 = 0 + 79 Reorder the terms: -79 + 79 + -6y + y2 = 0 + 79 Combine like terms: -79 + 79 = 0 0 + -6y + y2 = 0 + 79 -6y + y2 = 0 + 79 Combine like terms: 0 + 79 = 79 -6y + y2 = 79 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 = 79 + 9 Reorder the terms: 9 + -6y + y2 = 79 + 9 Combine like terms: 79 + 9 = 88 9 + -6y + y2 = 88 Factor a perfect square on the left side: (y + -3)(y + -3) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (y + -3) equal to 9.38083152 and -9.38083152.Subproblem 1
y + -3 = 9.38083152 Simplifying y + -3 = 9.38083152 Reorder the terms: -3 + y = 9.38083152 Solving -3 + y = 9.38083152 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 = 9.38083152 + 3 Combine like terms: -3 + 3 = 0 0 + y = 9.38083152 + 3 y = 9.38083152 + 3 Combine like terms: 9.38083152 + 3 = 12.38083152 y = 12.38083152 Simplifying y = 12.38083152Subproblem 2
y + -3 = -9.38083152 Simplifying y + -3 = -9.38083152 Reorder the terms: -3 + y = -9.38083152 Solving -3 + y = -9.38083152 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 = -9.38083152 + 3 Combine like terms: -3 + 3 = 0 0 + y = -9.38083152 + 3 y = -9.38083152 + 3 Combine like terms: -9.38083152 + 3 = -6.38083152 y = -6.38083152 Simplifying y = -6.38083152Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.38083152, -6.38083152}
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