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Simplifying y2 + -62y = -126 Reorder the terms: -62y + y2 = -126 Solving -62y + y2 = -126 Solving for variable 'y'. Reorder the terms: 126 + -62y + y2 = -126 + 126 Combine like terms: -126 + 126 = 0 126 + -62y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-126' to each side of the equation. 126 + -62y + -126 + y2 = 0 + -126 Reorder the terms: 126 + -126 + -62y + y2 = 0 + -126 Combine like terms: 126 + -126 = 0 0 + -62y + y2 = 0 + -126 -62y + y2 = 0 + -126 Combine like terms: 0 + -126 = -126 -62y + y2 = -126 The y term is -62y. Take half its coefficient (-31). Square it (961) and add it to both sides. Add '961' to each side of the equation. -62y + 961 + y2 = -126 + 961 Reorder the terms: 961 + -62y + y2 = -126 + 961 Combine like terms: -126 + 961 = 835 961 + -62y + y2 = 835 Factor a perfect square on the left side: (y + -31)(y + -31) = 835 Calculate the square root of the right side: 28.896366554 Break this problem into two subproblems by setting (y + -31) equal to 28.896366554 and -28.896366554.Subproblem 1
y + -31 = 28.896366554 Simplifying y + -31 = 28.896366554 Reorder the terms: -31 + y = 28.896366554 Solving -31 + y = 28.896366554 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + y = 28.896366554 + 31 Combine like terms: -31 + 31 = 0 0 + y = 28.896366554 + 31 y = 28.896366554 + 31 Combine like terms: 28.896366554 + 31 = 59.896366554 y = 59.896366554 Simplifying y = 59.896366554Subproblem 2
y + -31 = -28.896366554 Simplifying y + -31 = -28.896366554 Reorder the terms: -31 + y = -28.896366554 Solving -31 + y = -28.896366554 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + y = -28.896366554 + 31 Combine like terms: -31 + 31 = 0 0 + y = -28.896366554 + 31 y = -28.896366554 + 31 Combine like terms: -28.896366554 + 31 = 2.103633446 y = 2.103633446 Simplifying y = 2.103633446Solution
The solution to the problem is based on the solutions from the subproblems. y = {59.896366554, 2.103633446}
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