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Simplifying y2 + 24y + 21 = 0 Reorder the terms: 21 + 24y + y2 = 0 Solving 21 + 24y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + 24y + -21 + y2 = 0 + -21 Reorder the terms: 21 + -21 + 24y + y2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + 24y + y2 = 0 + -21 24y + y2 = 0 + -21 Combine like terms: 0 + -21 = -21 24y + y2 = -21 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 = -21 + 144 Reorder the terms: 144 + 24y + y2 = -21 + 144 Combine like terms: -21 + 144 = 123 144 + 24y + y2 = 123 Factor a perfect square on the left side: (y + 12)(y + 12) = 123 Calculate the square root of the right side: 11.090536506 Break this problem into two subproblems by setting (y + 12) equal to 11.090536506 and -11.090536506.Subproblem 1
y + 12 = 11.090536506 Simplifying y + 12 = 11.090536506 Reorder the terms: 12 + y = 11.090536506 Solving 12 + y = 11.090536506 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 = 11.090536506 + -12 Combine like terms: 12 + -12 = 0 0 + y = 11.090536506 + -12 y = 11.090536506 + -12 Combine like terms: 11.090536506 + -12 = -0.909463494 y = -0.909463494 Simplifying y = -0.909463494Subproblem 2
y + 12 = -11.090536506 Simplifying y + 12 = -11.090536506 Reorder the terms: 12 + y = -11.090536506 Solving 12 + y = -11.090536506 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 = -11.090536506 + -12 Combine like terms: 12 + -12 = 0 0 + y = -11.090536506 + -12 y = -11.090536506 + -12 Combine like terms: -11.090536506 + -12 = -23.090536506 y = -23.090536506 Simplifying y = -23.090536506Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.909463494, -23.090536506}
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