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Simplifying 8y2 + 3y + -6 = 0 Reorder the terms: -6 + 3y + 8y2 = 0 Solving -6 + 3y + 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'. -0.75 + 0.375y + y2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 0.375y + 0.75 + y2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 0.375y + y2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 0.375y + y2 = 0 + 0.75 0.375y + y2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 0.375y + y2 = 0.75 The y term is 0.375y. Take half its coefficient (0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. 0.375y + 0.03515625 + y2 = 0.75 + 0.03515625 Reorder the terms: 0.03515625 + 0.375y + y2 = 0.75 + 0.03515625 Combine like terms: 0.75 + 0.03515625 = 0.78515625 0.03515625 + 0.375y + y2 = 0.78515625 Factor a perfect square on the left side: (y + 0.1875)(y + 0.1875) = 0.78515625 Calculate the square root of the right side: 0.88609043 Break this problem into two subproblems by setting (y + 0.1875) equal to 0.88609043 and -0.88609043.Subproblem 1
y + 0.1875 = 0.88609043 Simplifying y + 0.1875 = 0.88609043 Reorder the terms: 0.1875 + y = 0.88609043 Solving 0.1875 + y = 0.88609043 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + y = 0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + y = 0.88609043 + -0.1875 y = 0.88609043 + -0.1875 Combine like terms: 0.88609043 + -0.1875 = 0.69859043 y = 0.69859043 Simplifying y = 0.69859043Subproblem 2
y + 0.1875 = -0.88609043 Simplifying y + 0.1875 = -0.88609043 Reorder the terms: 0.1875 + y = -0.88609043 Solving 0.1875 + y = -0.88609043 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + y = -0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + y = -0.88609043 + -0.1875 y = -0.88609043 + -0.1875 Combine like terms: -0.88609043 + -0.1875 = -1.07359043 y = -1.07359043 Simplifying y = -1.07359043Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.69859043, -1.07359043}
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