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Simplifying y2 + -6y + 3 = 81 Reorder the terms: 3 + -6y + y2 = 81 Solving 3 + -6y + y2 = 81 Solving for variable 'y'. Reorder the terms: 3 + -81 + -6y + y2 = 81 + -81 Combine like terms: 3 + -81 = -78 -78 + -6y + y2 = 81 + -81 Combine like terms: 81 + -81 = 0 -78 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -6y + 78 + y2 = 0 + 78 Reorder the terms: -78 + 78 + -6y + y2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -6y + y2 = 0 + 78 -6y + y2 = 0 + 78 Combine like terms: 0 + 78 = 78 -6y + y2 = 78 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 = 78 + 9 Reorder the terms: 9 + -6y + y2 = 78 + 9 Combine like terms: 78 + 9 = 87 9 + -6y + y2 = 87 Factor a perfect square on the left side: (y + -3)(y + -3) = 87 Calculate the square root of the right side: 9.327379053 Break this problem into two subproblems by setting (y + -3) equal to 9.327379053 and -9.327379053.Subproblem 1
y + -3 = 9.327379053 Simplifying y + -3 = 9.327379053 Reorder the terms: -3 + y = 9.327379053 Solving -3 + y = 9.327379053 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 = 9.327379053 + 3 Combine like terms: -3 + 3 = 0 0 + y = 9.327379053 + 3 y = 9.327379053 + 3 Combine like terms: 9.327379053 + 3 = 12.327379053 y = 12.327379053 Simplifying y = 12.327379053Subproblem 2
y + -3 = -9.327379053 Simplifying y + -3 = -9.327379053 Reorder the terms: -3 + y = -9.327379053 Solving -3 + y = -9.327379053 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 = -9.327379053 + 3 Combine like terms: -3 + 3 = 0 0 + y = -9.327379053 + 3 y = -9.327379053 + 3 Combine like terms: -9.327379053 + 3 = -6.327379053 y = -6.327379053 Simplifying y = -6.327379053Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.327379053, -6.327379053}
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