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Simplifying y * y + 12y = 55 Multiply y * y y2 + 12y = 55 Reorder the terms: 12y + y2 = 55 Solving 12y + y2 = 55 Solving for variable 'y'. Reorder the terms: -55 + 12y + y2 = 55 + -55 Combine like terms: 55 + -55 = 0 -55 + 12y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 12y + 55 + y2 = 0 + 55 Reorder the terms: -55 + 55 + 12y + y2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 12y + y2 = 0 + 55 12y + y2 = 0 + 55 Combine like terms: 0 + 55 = 55 12y + y2 = 55 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 = 55 + 36 Reorder the terms: 36 + 12y + y2 = 55 + 36 Combine like terms: 55 + 36 = 91 36 + 12y + y2 = 91 Factor a perfect square on the left side: (y + 6)(y + 6) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (y + 6) equal to 9.539392014 and -9.539392014.Subproblem 1
y + 6 = 9.539392014 Simplifying y + 6 = 9.539392014 Reorder the terms: 6 + y = 9.539392014 Solving 6 + y = 9.539392014 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 = 9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + y = 9.539392014 + -6 y = 9.539392014 + -6 Combine like terms: 9.539392014 + -6 = 3.539392014 y = 3.539392014 Simplifying y = 3.539392014Subproblem 2
y + 6 = -9.539392014 Simplifying y + 6 = -9.539392014 Reorder the terms: 6 + y = -9.539392014 Solving 6 + y = -9.539392014 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 = -9.539392014 + -6 Combine like terms: 6 + -6 = 0 0 + y = -9.539392014 + -6 y = -9.539392014 + -6 Combine like terms: -9.539392014 + -6 = -15.539392014 y = -15.539392014 Simplifying y = -15.539392014Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.539392014, -15.539392014}
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