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Simplifying 2y2 + -26y + 69 = 0 Reorder the terms: 69 + -26y + 2y2 = 0 Solving 69 + -26y + 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'. 34.5 + -13y + y2 = 0 Move the constant term to the right: Add '-34.5' to each side of the equation. 34.5 + -13y + -34.5 + y2 = 0 + -34.5 Reorder the terms: 34.5 + -34.5 + -13y + y2 = 0 + -34.5 Combine like terms: 34.5 + -34.5 = 0.0 0.0 + -13y + y2 = 0 + -34.5 -13y + y2 = 0 + -34.5 Combine like terms: 0 + -34.5 = -34.5 -13y + y2 = -34.5 The y term is -13y. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13y + 42.25 + y2 = -34.5 + 42.25 Reorder the terms: 42.25 + -13y + y2 = -34.5 + 42.25 Combine like terms: -34.5 + 42.25 = 7.75 42.25 + -13y + y2 = 7.75 Factor a perfect square on the left side: (y + -6.5)(y + -6.5) = 7.75 Calculate the square root of the right side: 2.783882181 Break this problem into two subproblems by setting (y + -6.5) equal to 2.783882181 and -2.783882181.Subproblem 1
y + -6.5 = 2.783882181 Simplifying y + -6.5 = 2.783882181 Reorder the terms: -6.5 + y = 2.783882181 Solving -6.5 + y = 2.783882181 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = 2.783882181 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = 2.783882181 + 6.5 y = 2.783882181 + 6.5 Combine like terms: 2.783882181 + 6.5 = 9.283882181 y = 9.283882181 Simplifying y = 9.283882181Subproblem 2
y + -6.5 = -2.783882181 Simplifying y + -6.5 = -2.783882181 Reorder the terms: -6.5 + y = -2.783882181 Solving -6.5 + y = -2.783882181 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + y = -2.783882181 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + y = -2.783882181 + 6.5 y = -2.783882181 + 6.5 Combine like terms: -2.783882181 + 6.5 = 3.716117819 y = 3.716117819 Simplifying y = 3.716117819Solution
The solution to the problem is based on the solutions from the subproblems. y = {9.283882181, 3.716117819}
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