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Simplifying 8y2 + -10y + -9 = 0 Reorder the terms: -9 + -10y + 8y2 = 0 Solving -9 + -10y + 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'. -1.125 + -1.25y + y2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -1.25y + 1.125 + y2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -1.25y + y2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -1.25y + y2 = 0 + 1.125 -1.25y + y2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -1.25y + y2 = 1.125 The y term is -1.25y. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25y + 0.390625 + y2 = 1.125 + 0.390625 Reorder the terms: 0.390625 + -1.25y + y2 = 1.125 + 0.390625 Combine like terms: 1.125 + 0.390625 = 1.515625 0.390625 + -1.25y + y2 = 1.515625 Factor a perfect square on the left side: (y + -0.625)(y + -0.625) = 1.515625 Calculate the square root of the right side: 1.231107225 Break this problem into two subproblems by setting (y + -0.625) equal to 1.231107225 and -1.231107225.Subproblem 1
y + -0.625 = 1.231107225 Simplifying y + -0.625 = 1.231107225 Reorder the terms: -0.625 + y = 1.231107225 Solving -0.625 + y = 1.231107225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = 1.231107225 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = 1.231107225 + 0.625 y = 1.231107225 + 0.625 Combine like terms: 1.231107225 + 0.625 = 1.856107225 y = 1.856107225 Simplifying y = 1.856107225Subproblem 2
y + -0.625 = -1.231107225 Simplifying y + -0.625 = -1.231107225 Reorder the terms: -0.625 + y = -1.231107225 Solving -0.625 + y = -1.231107225 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + y = -1.231107225 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + y = -1.231107225 + 0.625 y = -1.231107225 + 0.625 Combine like terms: -1.231107225 + 0.625 = -0.606107225 y = -0.606107225 Simplifying y = -0.606107225Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.856107225, -0.606107225}
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