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Simplifying 4y2 + -8y = 13 Reorder the terms: -8y + 4y2 = 13 Solving -8y + 4y2 = 13 Solving for variable 'y'. Reorder the terms: -13 + -8y + 4y2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -8y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.25 + -2y + y2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -2y + 3.25 + y2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -2y + y2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -2y + y2 = 0 + 3.25 -2y + y2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -2y + y2 = 3.25 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 3.25 + 1 Reorder the terms: 1 + -2y + y2 = 3.25 + 1 Combine like terms: 3.25 + 1 = 4.25 1 + -2y + y2 = 4.25 Factor a perfect square on the left side: (y + -1)(y + -1) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (y + -1) equal to 2.061552813 and -2.061552813.Subproblem 1
y + -1 = 2.061552813 Simplifying y + -1 = 2.061552813 Reorder the terms: -1 + y = 2.061552813 Solving -1 + y = 2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.061552813 + 1 y = 2.061552813 + 1 Combine like terms: 2.061552813 + 1 = 3.061552813 y = 3.061552813 Simplifying y = 3.061552813Subproblem 2
y + -1 = -2.061552813 Simplifying y + -1 = -2.061552813 Reorder the terms: -1 + y = -2.061552813 Solving -1 + y = -2.061552813 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -2.061552813 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.061552813 + 1 y = -2.061552813 + 1 Combine like terms: -2.061552813 + 1 = -1.061552813 y = -1.061552813 Simplifying y = -1.061552813Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.061552813, -1.061552813}
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