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Simplifying y2 + 12y + 13 = 2y2 + 4 Reorder the terms: 13 + 12y + y2 = 2y2 + 4 Reorder the terms: 13 + 12y + y2 = 4 + 2y2 Solving 13 + 12y + y2 = 4 + 2y2 Solving for variable 'y'. Reorder the terms: 13 + -4 + 12y + y2 + -2y2 = 4 + 2y2 + -4 + -2y2 Combine like terms: 13 + -4 = 9 9 + 12y + y2 + -2y2 = 4 + 2y2 + -4 + -2y2 Combine like terms: y2 + -2y2 = -1y2 9 + 12y + -1y2 = 4 + 2y2 + -4 + -2y2 Reorder the terms: 9 + 12y + -1y2 = 4 + -4 + 2y2 + -2y2 Combine like terms: 4 + -4 = 0 9 + 12y + -1y2 = 0 + 2y2 + -2y2 9 + 12y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 9 + 12y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -9 + -12y + y2 = 0 Move the constant term to the right: Add '9' to each side of the equation. -9 + -12y + 9 + y2 = 0 + 9 Reorder the terms: -9 + 9 + -12y + y2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -12y + y2 = 0 + 9 -12y + y2 = 0 + 9 Combine like terms: 0 + 9 = 9 -12y + y2 = 9 The y term is -12y. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12y + 36 + y2 = 9 + 36 Reorder the terms: 36 + -12y + y2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + -12y + y2 = 45 Factor a perfect square on the left side: (y + -6)(y + -6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (y + -6) equal to 6.708203933 and -6.708203933.Subproblem 1
y + -6 = 6.708203933 Simplifying y + -6 = 6.708203933 Reorder the terms: -6 + y = 6.708203933 Solving -6 + y = 6.708203933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = 6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + y = 6.708203933 + 6 y = 6.708203933 + 6 Combine like terms: 6.708203933 + 6 = 12.708203933 y = 12.708203933 Simplifying y = 12.708203933Subproblem 2
y + -6 = -6.708203933 Simplifying y + -6 = -6.708203933 Reorder the terms: -6 + y = -6.708203933 Solving -6 + y = -6.708203933 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + y = -6.708203933 + 6 Combine like terms: -6 + 6 = 0 0 + y = -6.708203933 + 6 y = -6.708203933 + 6 Combine like terms: -6.708203933 + 6 = -0.708203933 y = -0.708203933 Simplifying y = -0.708203933Solution
The solution to the problem is based on the solutions from the subproblems. y = {12.708203933, -0.708203933}
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