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Simplifying y2 + -8 = 4y Reorder the terms: -8 + y2 = 4y Solving -8 + y2 = 4y Solving for variable 'y'. Reorder the terms: -8 + -4y + y2 = 4y + -4y Combine like terms: 4y + -4y = 0 -8 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -4y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -4y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -4y + y2 = 0 + 8 -4y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -4y + y2 = 8 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 8 + 4 Reorder the terms: 4 + -4y + y2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + -4y + y2 = 12 Factor a perfect square on the left side: (y + -2)(y + -2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + -2) equal to 3.464101615 and -3.464101615.Subproblem 1
y + -2 = 3.464101615 Simplifying y + -2 = 3.464101615 Reorder the terms: -2 + y = 3.464101615 Solving -2 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + y = 3.464101615 + 2 y = 3.464101615 + 2 Combine like terms: 3.464101615 + 2 = 5.464101615 y = 5.464101615 Simplifying y = 5.464101615Subproblem 2
y + -2 = -3.464101615 Simplifying y + -2 = -3.464101615 Reorder the terms: -2 + y = -3.464101615 Solving -2 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -3.464101615 + 2 Combine like terms: -2 + 2 = 0 0 + y = -3.464101615 + 2 y = -3.464101615 + 2 Combine like terms: -3.464101615 + 2 = -1.464101615 y = -1.464101615 Simplifying y = -1.464101615Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.464101615, -1.464101615}
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