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Simplifying 4y + -1y2 = 4 + -4y Solving 4y + -1y2 = 4 + -4y Solving for variable 'y'. Reorder the terms: -4 + 4y + 4y + -1y2 = 4 + -4y + -4 + 4y Combine like terms: 4y + 4y = 8y -4 + 8y + -1y2 = 4 + -4y + -4 + 4y Reorder the terms: -4 + 8y + -1y2 = 4 + -4 + -4y + 4y Combine like terms: 4 + -4 = 0 -4 + 8y + -1y2 = 0 + -4y + 4y -4 + 8y + -1y2 = -4y + 4y Combine like terms: -4y + 4y = 0 -4 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -8y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -8y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -8y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -8y + y2 = 0 + -4 -8y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -8y + y2 = -4 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = -4 + 16 Reorder the terms: 16 + -8y + y2 = -4 + 16 Combine like terms: -4 + 16 = 12 16 + -8y + y2 = 12 Factor a perfect square on the left side: (y + -4)(y + -4) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (y + -4) equal to 3.464101615 and -3.464101615.Subproblem 1
y + -4 = 3.464101615 Simplifying y + -4 = 3.464101615 Reorder the terms: -4 + y = 3.464101615 Solving -4 + y = 3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + y = 3.464101615 + 4 y = 3.464101615 + 4 Combine like terms: 3.464101615 + 4 = 7.464101615 y = 7.464101615 Simplifying y = 7.464101615Subproblem 2
y + -4 = -3.464101615 Simplifying y + -4 = -3.464101615 Reorder the terms: -4 + y = -3.464101615 Solving -4 + y = -3.464101615 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -3.464101615 + 4 Combine like terms: -4 + 4 = 0 0 + y = -3.464101615 + 4 y = -3.464101615 + 4 Combine like terms: -3.464101615 + 4 = 0.535898385 y = 0.535898385 Simplifying y = 0.535898385Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.464101615, 0.535898385}
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