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Simplifying 2y2 + -20y + -525 = 0 Reorder the terms: -525 + -20y + 2y2 = 0 Solving -525 + -20y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -262.5 + -10y + y2 = 0 Move the constant term to the right: Add '262.5' to each side of the equation. -262.5 + -10y + 262.5 + y2 = 0 + 262.5 Reorder the terms: -262.5 + 262.5 + -10y + y2 = 0 + 262.5 Combine like terms: -262.5 + 262.5 = 0.0 0.0 + -10y + y2 = 0 + 262.5 -10y + y2 = 0 + 262.5 Combine like terms: 0 + 262.5 = 262.5 -10y + y2 = 262.5 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 = 262.5 + 25 Reorder the terms: 25 + -10y + y2 = 262.5 + 25 Combine like terms: 262.5 + 25 = 287.5 25 + -10y + y2 = 287.5 Factor a perfect square on the left side: (y + -5)(y + -5) = 287.5 Calculate the square root of the right side: 16.955824958 Break this problem into two subproblems by setting (y + -5) equal to 16.955824958 and -16.955824958.Subproblem 1
y + -5 = 16.955824958 Simplifying y + -5 = 16.955824958 Reorder the terms: -5 + y = 16.955824958 Solving -5 + y = 16.955824958 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 = 16.955824958 + 5 Combine like terms: -5 + 5 = 0 0 + y = 16.955824958 + 5 y = 16.955824958 + 5 Combine like terms: 16.955824958 + 5 = 21.955824958 y = 21.955824958 Simplifying y = 21.955824958Subproblem 2
y + -5 = -16.955824958 Simplifying y + -5 = -16.955824958 Reorder the terms: -5 + y = -16.955824958 Solving -5 + y = -16.955824958 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 = -16.955824958 + 5 Combine like terms: -5 + 5 = 0 0 + y = -16.955824958 + 5 y = -16.955824958 + 5 Combine like terms: -16.955824958 + 5 = -11.955824958 y = -11.955824958 Simplifying y = -11.955824958Solution
The solution to the problem is based on the solutions from the subproblems. y = {21.955824958, -11.955824958}
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