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Simplifying 0.8y2 + 8y = 12 Reorder the terms: 8y + 0.8y2 = 12 Solving 8y + 0.8y2 = 12 Solving for variable 'y'. Reorder the terms: -12 + 8y + 0.8y2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 8y + 0.8y2 = 0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -15 + 10y + y2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + 10y + 15 + y2 = 0 + 15 Reorder the terms: -15 + 15 + 10y + y2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 10y + y2 = 0 + 15 10y + y2 = 0 + 15 Combine like terms: 0 + 15 = 15 10y + y2 = 15 The y term is 10y. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10y + 25 + y2 = 15 + 25 Reorder the terms: 25 + 10y + y2 = 15 + 25 Combine like terms: 15 + 25 = 40 25 + 10y + y2 = 40 Factor a perfect square on the left side: (y + 5)(y + 5) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (y + 5) equal to 6.32455532 and -6.32455532.Subproblem 1
y + 5 = 6.32455532 Simplifying y + 5 = 6.32455532 Reorder the terms: 5 + y = 6.32455532 Solving 5 + y = 6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = 6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + y = 6.32455532 + -5 y = 6.32455532 + -5 Combine like terms: 6.32455532 + -5 = 1.32455532 y = 1.32455532 Simplifying y = 1.32455532Subproblem 2
y + 5 = -6.32455532 Simplifying y + 5 = -6.32455532 Reorder the terms: 5 + y = -6.32455532 Solving 5 + y = -6.32455532 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + y = -6.32455532 + -5 Combine like terms: 5 + -5 = 0 0 + y = -6.32455532 + -5 y = -6.32455532 + -5 Combine like terms: -6.32455532 + -5 = -11.32455532 y = -11.32455532 Simplifying y = -11.32455532Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.32455532, -11.32455532}
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