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Simplifying y2 + -10y + 20 = 0 Reorder the terms: 20 + -10y + y2 = 0 Solving 20 + -10y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-20' to each side of the equation. 20 + -10y + -20 + y2 = 0 + -20 Reorder the terms: 20 + -20 + -10y + y2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -10y + y2 = 0 + -20 -10y + y2 = 0 + -20 Combine like terms: 0 + -20 = -20 -10y + y2 = -20 The y term is -10y. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10y + 25 + y2 = -20 + 25 Reorder the terms: 25 + -10y + y2 = -20 + 25 Combine like terms: -20 + 25 = 5 25 + -10y + y2 = 5 Factor a perfect square on the left side: (y + -5)(y + -5) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (y + -5) equal to 2.236067978 and -2.236067978.Subproblem 1
y + -5 = 2.236067978 Simplifying y + -5 = 2.236067978 Reorder the terms: -5 + y = 2.236067978 Solving -5 + y = 2.236067978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + y = 2.236067978 + 5 y = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 y = 7.236067978 Simplifying y = 7.236067978Subproblem 2
y + -5 = -2.236067978 Simplifying y + -5 = -2.236067978 Reorder the terms: -5 + y = -2.236067978 Solving -5 + y = -2.236067978 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + y = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + y = -2.236067978 + 5 y = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 y = 2.763932022 Simplifying y = 2.763932022Solution
The solution to the problem is based on the solutions from the subproblems. y = {7.236067978, 2.763932022}
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