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Simplifying 2y2 + -13y + 14 = 0 Reorder the terms: 14 + -13y + 2y2 = 0 Solving 14 + -13y + 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'. 7 + -6.5y + y2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -6.5y + -7 + y2 = 0 + -7 Reorder the terms: 7 + -7 + -6.5y + y2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6.5y + y2 = 0 + -7 -6.5y + y2 = 0 + -7 Combine like terms: 0 + -7 = -7 -6.5y + y2 = -7 The y term is -6.5y. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5y + 10.5625 + y2 = -7 + 10.5625 Reorder the terms: 10.5625 + -6.5y + y2 = -7 + 10.5625 Combine like terms: -7 + 10.5625 = 3.5625 10.5625 + -6.5y + y2 = 3.5625 Factor a perfect square on the left side: (y + -3.25)(y + -3.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (y + -3.25) equal to 1.887458609 and -1.887458609.Subproblem 1
y + -3.25 = 1.887458609 Simplifying y + -3.25 = 1.887458609 Reorder the terms: -3.25 + y = 1.887458609 Solving -3.25 + y = 1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = 1.887458609 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = 1.887458609 + 3.25 y = 1.887458609 + 3.25 Combine like terms: 1.887458609 + 3.25 = 5.137458609 y = 5.137458609 Simplifying y = 5.137458609Subproblem 2
y + -3.25 = -1.887458609 Simplifying y + -3.25 = -1.887458609 Reorder the terms: -3.25 + y = -1.887458609 Solving -3.25 + y = -1.887458609 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + y = -1.887458609 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + y = -1.887458609 + 3.25 y = -1.887458609 + 3.25 Combine like terms: -1.887458609 + 3.25 = 1.362541391 y = 1.362541391 Simplifying y = 1.362541391Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.137458609, 1.362541391}
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