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Simplifying y2 + 24y = 29 Reorder the terms: 24y + y2 = 29 Solving 24y + y2 = 29 Solving for variable 'y'. Reorder the terms: -29 + 24y + y2 = 29 + -29 Combine like terms: 29 + -29 = 0 -29 + 24y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + 24y + 29 + y2 = 0 + 29 Reorder the terms: -29 + 29 + 24y + y2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + 24y + y2 = 0 + 29 24y + y2 = 0 + 29 Combine like terms: 0 + 29 = 29 24y + y2 = 29 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 = 29 + 144 Reorder the terms: 144 + 24y + y2 = 29 + 144 Combine like terms: 29 + 144 = 173 144 + 24y + y2 = 173 Factor a perfect square on the left side: (y + 12)(y + 12) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (y + 12) equal to 13.152946438 and -13.152946438.Subproblem 1
y + 12 = 13.152946438 Simplifying y + 12 = 13.152946438 Reorder the terms: 12 + y = 13.152946438 Solving 12 + y = 13.152946438 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 = 13.152946438 + -12 Combine like terms: 12 + -12 = 0 0 + y = 13.152946438 + -12 y = 13.152946438 + -12 Combine like terms: 13.152946438 + -12 = 1.152946438 y = 1.152946438 Simplifying y = 1.152946438Subproblem 2
y + 12 = -13.152946438 Simplifying y + 12 = -13.152946438 Reorder the terms: 12 + y = -13.152946438 Solving 12 + y = -13.152946438 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 = -13.152946438 + -12 Combine like terms: 12 + -12 = 0 0 + y = -13.152946438 + -12 y = -13.152946438 + -12 Combine like terms: -13.152946438 + -12 = -25.152946438 y = -25.152946438 Simplifying y = -25.152946438Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.152946438, -25.152946438}
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