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Simplifying 5y2 + -20y + 13 = 0 Reorder the terms: 13 + -20y + 5y2 = 0 Solving 13 + -20y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.6 + -4y + y2 = 0 Move the constant term to the right: Add '-2.6' to each side of the equation. 2.6 + -4y + -2.6 + y2 = 0 + -2.6 Reorder the terms: 2.6 + -2.6 + -4y + y2 = 0 + -2.6 Combine like terms: 2.6 + -2.6 = 0.0 0.0 + -4y + y2 = 0 + -2.6 -4y + y2 = 0 + -2.6 Combine like terms: 0 + -2.6 = -2.6 -4y + y2 = -2.6 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -2.6 + 4 Reorder the terms: 4 + -4y + y2 = -2.6 + 4 Combine like terms: -2.6 + 4 = 1.4 4 + -4y + y2 = 1.4 Factor a perfect square on the left side: (y + -2)(y + -2) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (y + -2) equal to 1.183215957 and -1.183215957.Subproblem 1
y + -2 = 1.183215957 Simplifying y + -2 = 1.183215957 Reorder the terms: -2 + y = 1.183215957 Solving -2 + y = 1.183215957 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.183215957 + 2 y = 1.183215957 + 2 Combine like terms: 1.183215957 + 2 = 3.183215957 y = 3.183215957 Simplifying y = 3.183215957Subproblem 2
y + -2 = -1.183215957 Simplifying y + -2 = -1.183215957 Reorder the terms: -2 + y = -1.183215957 Solving -2 + y = -1.183215957 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.183215957 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.183215957 + 2 y = -1.183215957 + 2 Combine like terms: -1.183215957 + 2 = 0.816784043 y = 0.816784043 Simplifying y = 0.816784043Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.183215957, 0.816784043}
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