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Simplifying y2 + 12y + -49 = 0 Reorder the terms: -49 + 12y + y2 = 0 Solving -49 + 12y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 12y + 49 + y2 = 0 + 49 Reorder the terms: -49 + 49 + 12y + y2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 12y + y2 = 0 + 49 12y + y2 = 0 + 49 Combine like terms: 0 + 49 = 49 12y + y2 = 49 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 = 49 + 36 Reorder the terms: 36 + 12y + y2 = 49 + 36 Combine like terms: 49 + 36 = 85 36 + 12y + y2 = 85 Factor a perfect square on the left side: (y + 6)(y + 6) = 85 Calculate the square root of the right side: 9.219544457 Break this problem into two subproblems by setting (y + 6) equal to 9.219544457 and -9.219544457.Subproblem 1
y + 6 = 9.219544457 Simplifying y + 6 = 9.219544457 Reorder the terms: 6 + y = 9.219544457 Solving 6 + y = 9.219544457 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 = 9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + y = 9.219544457 + -6 y = 9.219544457 + -6 Combine like terms: 9.219544457 + -6 = 3.219544457 y = 3.219544457 Simplifying y = 3.219544457Subproblem 2
y + 6 = -9.219544457 Simplifying y + 6 = -9.219544457 Reorder the terms: 6 + y = -9.219544457 Solving 6 + y = -9.219544457 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 = -9.219544457 + -6 Combine like terms: 6 + -6 = 0 0 + y = -9.219544457 + -6 y = -9.219544457 + -6 Combine like terms: -9.219544457 + -6 = -15.219544457 y = -15.219544457 Simplifying y = -15.219544457Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.219544457, -15.219544457}
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