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Simplifying 0.25y2 + 2 * 0.25y = 10 + -1y Multiply 2 * 0.25 0.25y2 + 0.5y = 10 + -1y Reorder the terms: 0.5y + 0.25y2 = 10 + -1y Solving 0.5y + 0.25y2 = 10 + -1y Solving for variable 'y'. Reorder the terms: -10 + 0.5y + y + 0.25y2 = 10 + -1y + -10 + y Combine like terms: 0.5y + y = 1.5y -10 + 1.5y + 0.25y2 = 10 + -1y + -10 + y Reorder the terms: -10 + 1.5y + 0.25y2 = 10 + -10 + -1y + y Combine like terms: 10 + -10 = 0 -10 + 1.5y + 0.25y2 = 0 + -1y + y -10 + 1.5y + 0.25y2 = -1y + y Combine like terms: -1y + y = 0 -10 + 1.5y + 0.25y2 = 0 Begin completing the square. Divide all terms by 0.25 the coefficient of the squared term: Divide each side by '0.25'. -40 + 6y + y2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 6y + 40 + y2 = 0 + 40 Reorder the terms: -40 + 40 + 6y + y2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 6y + y2 = 0 + 40 6y + y2 = 0 + 40 Combine like terms: 0 + 40 = 40 6y + y2 = 40 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 40 + 9 Reorder the terms: 9 + 6y + y2 = 40 + 9 Combine like terms: 40 + 9 = 49 9 + 6y + y2 = 49 Factor a perfect square on the left side: (y + 3)(y + 3) = 49 Calculate the square root of the right side: 7 Break this problem into two subproblems by setting (y + 3) equal to 7 and -7.Subproblem 1
y + 3 = 7 Simplifying y + 3 = 7 Reorder the terms: 3 + y = 7 Solving 3 + y = 7 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 7 + -3 Combine like terms: 3 + -3 = 0 0 + y = 7 + -3 y = 7 + -3 Combine like terms: 7 + -3 = 4 y = 4 Simplifying y = 4Subproblem 2
y + 3 = -7 Simplifying y + 3 = -7 Reorder the terms: 3 + y = -7 Solving 3 + y = -7 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -7 + -3 Combine like terms: 3 + -3 = 0 0 + y = -7 + -3 y = -7 + -3 Combine like terms: -7 + -3 = -10 y = -10 Simplifying y = -10Solution
The solution to the problem is based on the solutions from the subproblems. y = {4, -10}
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