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Simplifying y2 + -6y = 46 Reorder the terms: -6y + y2 = 46 Solving -6y + y2 = 46 Solving for variable 'y'. Reorder the terms: -46 + -6y + y2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -6y + 46 + y2 = 0 + 46 Reorder the terms: -46 + 46 + -6y + y2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -6y + y2 = 0 + 46 -6y + y2 = 0 + 46 Combine like terms: 0 + 46 = 46 -6y + y2 = 46 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 = 46 + 9 Reorder the terms: 9 + -6y + y2 = 46 + 9 Combine like terms: 46 + 9 = 55 9 + -6y + y2 = 55 Factor a perfect square on the left side: (y + -3)(y + -3) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (y + -3) equal to 7.416198487 and -7.416198487.Subproblem 1
y + -3 = 7.416198487 Simplifying y + -3 = 7.416198487 Reorder the terms: -3 + y = 7.416198487 Solving -3 + y = 7.416198487 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 = 7.416198487 + 3 Combine like terms: -3 + 3 = 0 0 + y = 7.416198487 + 3 y = 7.416198487 + 3 Combine like terms: 7.416198487 + 3 = 10.416198487 y = 10.416198487 Simplifying y = 10.416198487Subproblem 2
y + -3 = -7.416198487 Simplifying y + -3 = -7.416198487 Reorder the terms: -3 + y = -7.416198487 Solving -3 + y = -7.416198487 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 = -7.416198487 + 3 Combine like terms: -3 + 3 = 0 0 + y = -7.416198487 + 3 y = -7.416198487 + 3 Combine like terms: -7.416198487 + 3 = -4.416198487 y = -4.416198487 Simplifying y = -4.416198487Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.416198487, -4.416198487}
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