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Simplifying y2 + 24y + -144 = 0 Reorder the terms: -144 + 24y + y2 = 0 Solving -144 + 24y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 24y + 144 + y2 = 0 + 144 Reorder the terms: -144 + 144 + 24y + y2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 24y + y2 = 0 + 144 24y + y2 = 0 + 144 Combine like terms: 0 + 144 = 144 24y + y2 = 144 The y term is 24y. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24y + 144 + y2 = 144 + 144 Reorder the terms: 144 + 24y + y2 = 144 + 144 Combine like terms: 144 + 144 = 288 144 + 24y + y2 = 288 Factor a perfect square on the left side: (y + 12)(y + 12) = 288 Calculate the square root of the right side: 16.970562748 Break this problem into two subproblems by setting (y + 12) equal to 16.970562748 and -16.970562748.Subproblem 1
y + 12 = 16.970562748 Simplifying y + 12 = 16.970562748 Reorder the terms: 12 + y = 16.970562748 Solving 12 + y = 16.970562748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + y = 16.970562748 + -12 Combine like terms: 12 + -12 = 0 0 + y = 16.970562748 + -12 y = 16.970562748 + -12 Combine like terms: 16.970562748 + -12 = 4.970562748 y = 4.970562748 Simplifying y = 4.970562748Subproblem 2
y + 12 = -16.970562748 Simplifying y + 12 = -16.970562748 Reorder the terms: 12 + y = -16.970562748 Solving 12 + y = -16.970562748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + y = -16.970562748 + -12 Combine like terms: 12 + -12 = 0 0 + y = -16.970562748 + -12 y = -16.970562748 + -12 Combine like terms: -16.970562748 + -12 = -28.970562748 y = -28.970562748 Simplifying y = -28.970562748Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.970562748, -28.970562748}
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