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Simplifying y2 + -29y = 54 Reorder the terms: -29y + y2 = 54 Solving -29y + y2 = 54 Solving for variable 'y'. Reorder the terms: -54 + -29y + y2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -29y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -29y + 54 + y2 = 0 + 54 Reorder the terms: -54 + 54 + -29y + y2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -29y + y2 = 0 + 54 -29y + y2 = 0 + 54 Combine like terms: 0 + 54 = 54 -29y + y2 = 54 The y term is -29y. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29y + 210.25 + y2 = 54 + 210.25 Reorder the terms: 210.25 + -29y + y2 = 54 + 210.25 Combine like terms: 54 + 210.25 = 264.25 210.25 + -29y + y2 = 264.25 Factor a perfect square on the left side: (y + -14.5)(y + -14.5) = 264.25 Calculate the square root of the right side: 16.255768207 Break this problem into two subproblems by setting (y + -14.5) equal to 16.255768207 and -16.255768207.Subproblem 1
y + -14.5 = 16.255768207 Simplifying y + -14.5 = 16.255768207 Reorder the terms: -14.5 + y = 16.255768207 Solving -14.5 + y = 16.255768207 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + y = 16.255768207 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + y = 16.255768207 + 14.5 y = 16.255768207 + 14.5 Combine like terms: 16.255768207 + 14.5 = 30.755768207 y = 30.755768207 Simplifying y = 30.755768207Subproblem 2
y + -14.5 = -16.255768207 Simplifying y + -14.5 = -16.255768207 Reorder the terms: -14.5 + y = -16.255768207 Solving -14.5 + y = -16.255768207 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + y = -16.255768207 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + y = -16.255768207 + 14.5 y = -16.255768207 + 14.5 Combine like terms: -16.255768207 + 14.5 = -1.755768207 y = -1.755768207 Simplifying y = -1.755768207Solution
The solution to the problem is based on the solutions from the subproblems. y = {30.755768207, -1.755768207}
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