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Simplifying y2 + -6y + -4 = 0 Reorder the terms: -4 + -6y + y2 = 0 Solving -4 + -6y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -6y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -6y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -6y + y2 = 0 + 4 -6y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -6y + y2 = 4 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 = 4 + 9 Reorder the terms: 9 + -6y + y2 = 4 + 9 Combine like terms: 4 + 9 = 13 9 + -6y + y2 = 13 Factor a perfect square on the left side: (y + -3)(y + -3) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (y + -3) equal to 3.605551275 and -3.605551275.Subproblem 1
y + -3 = 3.605551275 Simplifying y + -3 = 3.605551275 Reorder the terms: -3 + y = 3.605551275 Solving -3 + y = 3.605551275 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 = 3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + y = 3.605551275 + 3 y = 3.605551275 + 3 Combine like terms: 3.605551275 + 3 = 6.605551275 y = 6.605551275 Simplifying y = 6.605551275Subproblem 2
y + -3 = -3.605551275 Simplifying y + -3 = -3.605551275 Reorder the terms: -3 + y = -3.605551275 Solving -3 + y = -3.605551275 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 = -3.605551275 + 3 Combine like terms: -3 + 3 = 0 0 + y = -3.605551275 + 3 y = -3.605551275 + 3 Combine like terms: -3.605551275 + 3 = -0.605551275 y = -0.605551275 Simplifying y = -0.605551275Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.605551275, -0.605551275}
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