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Simplifying y2 + 4 = 2y2 + 8y + -1 Reorder the terms: 4 + y2 = 2y2 + 8y + -1 Reorder the terms: 4 + y2 = -1 + 8y + 2y2 Solving 4 + y2 = -1 + 8y + 2y2 Solving for variable 'y'. Reorder the terms: 4 + 1 + -8y + y2 + -2y2 = -1 + 8y + 2y2 + 1 + -8y + -2y2 Combine like terms: 4 + 1 = 5 5 + -8y + y2 + -2y2 = -1 + 8y + 2y2 + 1 + -8y + -2y2 Combine like terms: y2 + -2y2 = -1y2 5 + -8y + -1y2 = -1 + 8y + 2y2 + 1 + -8y + -2y2 Reorder the terms: 5 + -8y + -1y2 = -1 + 1 + 8y + -8y + 2y2 + -2y2 Combine like terms: -1 + 1 = 0 5 + -8y + -1y2 = 0 + 8y + -8y + 2y2 + -2y2 5 + -8y + -1y2 = 8y + -8y + 2y2 + -2y2 Combine like terms: 8y + -8y = 0 5 + -8y + -1y2 = 0 + 2y2 + -2y2 5 + -8y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 5 + -8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 8y + y2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 8y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + 8y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 8y + y2 = 0 + 5 8y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 8y + y2 = 5 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 = 5 + 16 Reorder the terms: 16 + 8y + y2 = 5 + 16 Combine like terms: 5 + 16 = 21 16 + 8y + y2 = 21 Factor a perfect square on the left side: (y + 4)(y + 4) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (y + 4) equal to 4.582575695 and -4.582575695.Subproblem 1
y + 4 = 4.582575695 Simplifying y + 4 = 4.582575695 Reorder the terms: 4 + y = 4.582575695 Solving 4 + y = 4.582575695 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 = 4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + y = 4.582575695 + -4 y = 4.582575695 + -4 Combine like terms: 4.582575695 + -4 = 0.582575695 y = 0.582575695 Simplifying y = 0.582575695Subproblem 2
y + 4 = -4.582575695 Simplifying y + 4 = -4.582575695 Reorder the terms: 4 + y = -4.582575695 Solving 4 + y = -4.582575695 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 = -4.582575695 + -4 Combine like terms: 4 + -4 = 0 0 + y = -4.582575695 + -4 y = -4.582575695 + -4 Combine like terms: -4.582575695 + -4 = -8.582575695 y = -8.582575695 Simplifying y = -8.582575695Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.582575695, -8.582575695}
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