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Simplifying y2 + 8y + -764 = 0 Reorder the terms: -764 + 8y + y2 = 0 Solving -764 + 8y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '764' to each side of the equation. -764 + 8y + 764 + y2 = 0 + 764 Reorder the terms: -764 + 764 + 8y + y2 = 0 + 764 Combine like terms: -764 + 764 = 0 0 + 8y + y2 = 0 + 764 8y + y2 = 0 + 764 Combine like terms: 0 + 764 = 764 8y + y2 = 764 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 = 764 + 16 Reorder the terms: 16 + 8y + y2 = 764 + 16 Combine like terms: 764 + 16 = 780 16 + 8y + y2 = 780 Factor a perfect square on the left side: (y + 4)(y + 4) = 780 Calculate the square root of the right side: 27.928480088 Break this problem into two subproblems by setting (y + 4) equal to 27.928480088 and -27.928480088.Subproblem 1
y + 4 = 27.928480088 Simplifying y + 4 = 27.928480088 Reorder the terms: 4 + y = 27.928480088 Solving 4 + y = 27.928480088 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 = 27.928480088 + -4 Combine like terms: 4 + -4 = 0 0 + y = 27.928480088 + -4 y = 27.928480088 + -4 Combine like terms: 27.928480088 + -4 = 23.928480088 y = 23.928480088 Simplifying y = 23.928480088Subproblem 2
y + 4 = -27.928480088 Simplifying y + 4 = -27.928480088 Reorder the terms: 4 + y = -27.928480088 Solving 4 + y = -27.928480088 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 = -27.928480088 + -4 Combine like terms: 4 + -4 = 0 0 + y = -27.928480088 + -4 y = -27.928480088 + -4 Combine like terms: -27.928480088 + -4 = -31.928480088 y = -31.928480088 Simplifying y = -31.928480088Solution
The solution to the problem is based on the solutions from the subproblems. y = {23.928480088, -31.928480088}
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