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Simplifying y2 + -29y + 64 = 0 Reorder the terms: 64 + -29y + y2 = 0 Solving 64 + -29y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -29y + -64 + y2 = 0 + -64 Reorder the terms: 64 + -64 + -29y + y2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -29y + y2 = 0 + -64 -29y + y2 = 0 + -64 Combine like terms: 0 + -64 = -64 -29y + y2 = -64 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 = -64 + 210.25 Reorder the terms: 210.25 + -29y + y2 = -64 + 210.25 Combine like terms: -64 + 210.25 = 146.25 210.25 + -29y + y2 = 146.25 Factor a perfect square on the left side: (y + -14.5)(y + -14.5) = 146.25 Calculate the square root of the right side: 12.093386622 Break this problem into two subproblems by setting (y + -14.5) equal to 12.093386622 and -12.093386622.Subproblem 1
y + -14.5 = 12.093386622 Simplifying y + -14.5 = 12.093386622 Reorder the terms: -14.5 + y = 12.093386622 Solving -14.5 + y = 12.093386622 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 = 12.093386622 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + y = 12.093386622 + 14.5 y = 12.093386622 + 14.5 Combine like terms: 12.093386622 + 14.5 = 26.593386622 y = 26.593386622 Simplifying y = 26.593386622Subproblem 2
y + -14.5 = -12.093386622 Simplifying y + -14.5 = -12.093386622 Reorder the terms: -14.5 + y = -12.093386622 Solving -14.5 + y = -12.093386622 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 = -12.093386622 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + y = -12.093386622 + 14.5 y = -12.093386622 + 14.5 Combine like terms: -12.093386622 + 14.5 = 2.406613378 y = 2.406613378 Simplifying y = 2.406613378Solution
The solution to the problem is based on the solutions from the subproblems. y = {26.593386622, 2.406613378}
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