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Simplifying y2 + -20y + 77 = 0 Reorder the terms: 77 + -20y + y2 = 0 Solving 77 + -20y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + -20y + -77 + y2 = 0 + -77 Reorder the terms: 77 + -77 + -20y + y2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + -20y + y2 = 0 + -77 -20y + y2 = 0 + -77 Combine like terms: 0 + -77 = -77 -20y + y2 = -77 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = -77 + 100 Reorder the terms: 100 + -20y + y2 = -77 + 100 Combine like terms: -77 + 100 = 23 100 + -20y + y2 = 23 Factor a perfect square on the left side: (y + -10)(y + -10) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (y + -10) equal to 4.795831523 and -4.795831523.Subproblem 1
y + -10 = 4.795831523 Simplifying y + -10 = 4.795831523 Reorder the terms: -10 + y = 4.795831523 Solving -10 + y = 4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 4.795831523 + 10 Combine like terms: -10 + 10 = 0 0 + y = 4.795831523 + 10 y = 4.795831523 + 10 Combine like terms: 4.795831523 + 10 = 14.795831523 y = 14.795831523 Simplifying y = 14.795831523Subproblem 2
y + -10 = -4.795831523 Simplifying y + -10 = -4.795831523 Reorder the terms: -10 + y = -4.795831523 Solving -10 + y = -4.795831523 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -4.795831523 + 10 Combine like terms: -10 + 10 = 0 0 + y = -4.795831523 + 10 y = -4.795831523 + 10 Combine like terms: -4.795831523 + 10 = 5.204168477 y = 5.204168477 Simplifying y = 5.204168477Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.795831523, 5.204168477}
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