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Simplifying y2 + 8y + 13 = 144 Reorder the terms: 13 + 8y + y2 = 144 Solving 13 + 8y + y2 = 144 Solving for variable 'y'. Reorder the terms: 13 + -144 + 8y + y2 = 144 + -144 Combine like terms: 13 + -144 = -131 -131 + 8y + y2 = 144 + -144 Combine like terms: 144 + -144 = 0 -131 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '131' to each side of the equation. -131 + 8y + 131 + y2 = 0 + 131 Reorder the terms: -131 + 131 + 8y + y2 = 0 + 131 Combine like terms: -131 + 131 = 0 0 + 8y + y2 = 0 + 131 8y + y2 = 0 + 131 Combine like terms: 0 + 131 = 131 8y + y2 = 131 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 131 + 16 Reorder the terms: 16 + 8y + y2 = 131 + 16 Combine like terms: 131 + 16 = 147 16 + 8y + y2 = 147 Factor a perfect square on the left side: (y + 4)(y + 4) = 147 Calculate the square root of the right side: 12.124355653 Break this problem into two subproblems by setting (y + 4) equal to 12.124355653 and -12.124355653.Subproblem 1
y + 4 = 12.124355653 Simplifying y + 4 = 12.124355653 Reorder the terms: 4 + y = 12.124355653 Solving 4 + y = 12.124355653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 12.124355653 + -4 Combine like terms: 4 + -4 = 0 0 + y = 12.124355653 + -4 y = 12.124355653 + -4 Combine like terms: 12.124355653 + -4 = 8.124355653 y = 8.124355653 Simplifying y = 8.124355653Subproblem 2
y + 4 = -12.124355653 Simplifying y + 4 = -12.124355653 Reorder the terms: 4 + y = -12.124355653 Solving 4 + y = -12.124355653 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -12.124355653 + -4 Combine like terms: 4 + -4 = 0 0 + y = -12.124355653 + -4 y = -12.124355653 + -4 Combine like terms: -12.124355653 + -4 = -16.124355653 y = -16.124355653 Simplifying y = -16.124355653Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.124355653, -16.124355653}
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