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Simplifying y2 + 5 = 578y Reorder the terms: 5 + y2 = 578y Solving 5 + y2 = 578y Solving for variable 'y'. Reorder the terms: 5 + -578y + y2 = 578y + -578y Combine like terms: 578y + -578y = 0 5 + -578y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -578y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -578y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -578y + y2 = 0 + -5 -578y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -578y + y2 = -5 The y term is -578y. Take half its coefficient (-289). Square it (83521) and add it to both sides. Add '83521' to each side of the equation. -578y + 83521 + y2 = -5 + 83521 Reorder the terms: 83521 + -578y + y2 = -5 + 83521 Combine like terms: -5 + 83521 = 83516 83521 + -578y + y2 = 83516 Factor a perfect square on the left side: (y + -289)(y + -289) = 83516 Calculate the square root of the right side: 288.991349351 Break this problem into two subproblems by setting (y + -289) equal to 288.991349351 and -288.991349351.Subproblem 1
y + -289 = 288.991349351 Simplifying y + -289 = 288.991349351 Reorder the terms: -289 + y = 288.991349351 Solving -289 + y = 288.991349351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '289' to each side of the equation. -289 + 289 + y = 288.991349351 + 289 Combine like terms: -289 + 289 = 0 0 + y = 288.991349351 + 289 y = 288.991349351 + 289 Combine like terms: 288.991349351 + 289 = 577.991349351 y = 577.991349351 Simplifying y = 577.991349351Subproblem 2
y + -289 = -288.991349351 Simplifying y + -289 = -288.991349351 Reorder the terms: -289 + y = -288.991349351 Solving -289 + y = -288.991349351 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '289' to each side of the equation. -289 + 289 + y = -288.991349351 + 289 Combine like terms: -289 + 289 = 0 0 + y = -288.991349351 + 289 y = -288.991349351 + 289 Combine like terms: -288.991349351 + 289 = 0.008650649 y = 0.008650649 Simplifying y = 0.008650649Solution
The solution to the problem is based on the solutions from the subproblems. y = {577.991349351, 0.008650649}
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