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Simplifying 8y2 + -23y + -15 = 0 Reorder the terms: -15 + -23y + 8y2 = 0 Solving -15 + -23y + 8y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.875 + -2.875y + y2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + -2.875y + 1.875 + y2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + -2.875y + y2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + -2.875y + y2 = 0 + 1.875 -2.875y + y2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 -2.875y + y2 = 1.875 The y term is -2.875y. Take half its coefficient (-1.4375). Square it (2.06640625) and add it to both sides. Add '2.06640625' to each side of the equation. -2.875y + 2.06640625 + y2 = 1.875 + 2.06640625 Reorder the terms: 2.06640625 + -2.875y + y2 = 1.875 + 2.06640625 Combine like terms: 1.875 + 2.06640625 = 3.94140625 2.06640625 + -2.875y + y2 = 3.94140625 Factor a perfect square on the left side: (y + -1.4375)(y + -1.4375) = 3.94140625 Calculate the square root of the right side: 1.985297522 Break this problem into two subproblems by setting (y + -1.4375) equal to 1.985297522 and -1.985297522.Subproblem 1
y + -1.4375 = 1.985297522 Simplifying y + -1.4375 = 1.985297522 Reorder the terms: -1.4375 + y = 1.985297522 Solving -1.4375 + y = 1.985297522 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + y = 1.985297522 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + y = 1.985297522 + 1.4375 y = 1.985297522 + 1.4375 Combine like terms: 1.985297522 + 1.4375 = 3.422797522 y = 3.422797522 Simplifying y = 3.422797522Subproblem 2
y + -1.4375 = -1.985297522 Simplifying y + -1.4375 = -1.985297522 Reorder the terms: -1.4375 + y = -1.985297522 Solving -1.4375 + y = -1.985297522 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.4375' to each side of the equation. -1.4375 + 1.4375 + y = -1.985297522 + 1.4375 Combine like terms: -1.4375 + 1.4375 = 0.0000 0.0000 + y = -1.985297522 + 1.4375 y = -1.985297522 + 1.4375 Combine like terms: -1.985297522 + 1.4375 = -0.547797522 y = -0.547797522 Simplifying y = -0.547797522Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.422797522, -0.547797522}
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