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Simplifying 3y2 + 18y + -25 = -3 Reorder the terms: -25 + 18y + 3y2 = -3 Solving -25 + 18y + 3y2 = -3 Solving for variable 'y'. Reorder the terms: -25 + 3 + 18y + 3y2 = -3 + 3 Combine like terms: -25 + 3 = -22 -22 + 18y + 3y2 = -3 + 3 Combine like terms: -3 + 3 = 0 -22 + 18y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -7.333333333 + 6y + y2 = 0 Move the constant term to the right: Add '7.333333333' to each side of the equation. -7.333333333 + 6y + 7.333333333 + y2 = 0 + 7.333333333 Reorder the terms: -7.333333333 + 7.333333333 + 6y + y2 = 0 + 7.333333333 Combine like terms: -7.333333333 + 7.333333333 = 0.000000000 0.000000000 + 6y + y2 = 0 + 7.333333333 6y + y2 = 0 + 7.333333333 Combine like terms: 0 + 7.333333333 = 7.333333333 6y + y2 = 7.333333333 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 = 7.333333333 + 9 Reorder the terms: 9 + 6y + y2 = 7.333333333 + 9 Combine like terms: 7.333333333 + 9 = 16.333333333 9 + 6y + y2 = 16.333333333 Factor a perfect square on the left side: (y + 3)(y + 3) = 16.333333333 Calculate the square root of the right side: 4.041451884 Break this problem into two subproblems by setting (y + 3) equal to 4.041451884 and -4.041451884.Subproblem 1
y + 3 = 4.041451884 Simplifying y + 3 = 4.041451884 Reorder the terms: 3 + y = 4.041451884 Solving 3 + y = 4.041451884 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 = 4.041451884 + -3 Combine like terms: 3 + -3 = 0 0 + y = 4.041451884 + -3 y = 4.041451884 + -3 Combine like terms: 4.041451884 + -3 = 1.041451884 y = 1.041451884 Simplifying y = 1.041451884Subproblem 2
y + 3 = -4.041451884 Simplifying y + 3 = -4.041451884 Reorder the terms: 3 + y = -4.041451884 Solving 3 + y = -4.041451884 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 = -4.041451884 + -3 Combine like terms: 3 + -3 = 0 0 + y = -4.041451884 + -3 y = -4.041451884 + -3 Combine like terms: -4.041451884 + -3 = -7.041451884 y = -7.041451884 Simplifying y = -7.041451884Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.041451884, -7.041451884}
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