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Simplifying y2 + -3y + -44 = 0 Reorder the terms: -44 + -3y + y2 = 0 Solving -44 + -3y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + -3y + 44 + y2 = 0 + 44 Reorder the terms: -44 + 44 + -3y + y2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -3y + y2 = 0 + 44 -3y + y2 = 0 + 44 Combine like terms: 0 + 44 = 44 -3y + y2 = 44 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 44 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 44 + 2.25 Combine like terms: 44 + 2.25 = 46.25 2.25 + -3y + y2 = 46.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (y + -1.5) equal to 6.800735254 and -6.800735254.Subproblem 1
y + -1.5 = 6.800735254 Simplifying y + -1.5 = 6.800735254 Reorder the terms: -1.5 + y = 6.800735254 Solving -1.5 + y = 6.800735254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 6.800735254 + 1.5 y = 6.800735254 + 1.5 Combine like terms: 6.800735254 + 1.5 = 8.300735254 y = 8.300735254 Simplifying y = 8.300735254Subproblem 2
y + -1.5 = -6.800735254 Simplifying y + -1.5 = -6.800735254 Reorder the terms: -1.5 + y = -6.800735254 Solving -1.5 + y = -6.800735254 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -6.800735254 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -6.800735254 + 1.5 y = -6.800735254 + 1.5 Combine like terms: -6.800735254 + 1.5 = -5.300735254 y = -5.300735254 Simplifying y = -5.300735254Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.300735254, -5.300735254}
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