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Simplifying 8y2 + 9y + -15 = 0 Reorder the terms: -15 + 9y + 8y2 = 0 Solving -15 + 9y + 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 + 1.125y + y2 = 0 Move the constant term to the right: Add '1.875' to each side of the equation. -1.875 + 1.125y + 1.875 + y2 = 0 + 1.875 Reorder the terms: -1.875 + 1.875 + 1.125y + y2 = 0 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + 1.125y + y2 = 0 + 1.875 1.125y + y2 = 0 + 1.875 Combine like terms: 0 + 1.875 = 1.875 1.125y + y2 = 1.875 The y term is 1.125y. Take half its coefficient (0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. 1.125y + 0.31640625 + y2 = 1.875 + 0.31640625 Reorder the terms: 0.31640625 + 1.125y + y2 = 1.875 + 0.31640625 Combine like terms: 1.875 + 0.31640625 = 2.19140625 0.31640625 + 1.125y + y2 = 2.19140625 Factor a perfect square on the left side: (y + 0.5625)(y + 0.5625) = 2.19140625 Calculate the square root of the right side: 1.48033991 Break this problem into two subproblems by setting (y + 0.5625) equal to 1.48033991 and -1.48033991.Subproblem 1
y + 0.5625 = 1.48033991 Simplifying y + 0.5625 = 1.48033991 Reorder the terms: 0.5625 + y = 1.48033991 Solving 0.5625 + y = 1.48033991 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = 1.48033991 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = 1.48033991 + -0.5625 y = 1.48033991 + -0.5625 Combine like terms: 1.48033991 + -0.5625 = 0.91783991 y = 0.91783991 Simplifying y = 0.91783991Subproblem 2
y + 0.5625 = -1.48033991 Simplifying y + 0.5625 = -1.48033991 Reorder the terms: 0.5625 + y = -1.48033991 Solving 0.5625 + y = -1.48033991 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.5625' to each side of the equation. 0.5625 + -0.5625 + y = -1.48033991 + -0.5625 Combine like terms: 0.5625 + -0.5625 = 0.0000 0.0000 + y = -1.48033991 + -0.5625 y = -1.48033991 + -0.5625 Combine like terms: -1.48033991 + -0.5625 = -2.04283991 y = -2.04283991 Simplifying y = -2.04283991Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.91783991, -2.04283991}
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