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Simplifying Y2 + -45Y + 30 = 0 Reorder the terms: 30 + -45Y + Y2 = 0 Solving 30 + -45Y + Y2 = 0 Solving for variable 'Y'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -45Y + -30 + Y2 = 0 + -30 Reorder the terms: 30 + -30 + -45Y + Y2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -45Y + Y2 = 0 + -30 -45Y + Y2 = 0 + -30 Combine like terms: 0 + -30 = -30 -45Y + Y2 = -30 The Y term is -45Y. Take half its coefficient (-22.5). Square it (506.25) and add it to both sides. Add '506.25' to each side of the equation. -45Y + 506.25 + Y2 = -30 + 506.25 Reorder the terms: 506.25 + -45Y + Y2 = -30 + 506.25 Combine like terms: -30 + 506.25 = 476.25 506.25 + -45Y + Y2 = 476.25 Factor a perfect square on the left side: (Y + -22.5)(Y + -22.5) = 476.25 Calculate the square root of the right side: 21.823152843 Break this problem into two subproblems by setting (Y + -22.5) equal to 21.823152843 and -21.823152843.Subproblem 1
Y + -22.5 = 21.823152843 Simplifying Y + -22.5 = 21.823152843 Reorder the terms: -22.5 + Y = 21.823152843 Solving -22.5 + Y = 21.823152843 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + Y = 21.823152843 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + Y = 21.823152843 + 22.5 Y = 21.823152843 + 22.5 Combine like terms: 21.823152843 + 22.5 = 44.323152843 Y = 44.323152843 Simplifying Y = 44.323152843Subproblem 2
Y + -22.5 = -21.823152843 Simplifying Y + -22.5 = -21.823152843 Reorder the terms: -22.5 + Y = -21.823152843 Solving -22.5 + Y = -21.823152843 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '22.5' to each side of the equation. -22.5 + 22.5 + Y = -21.823152843 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + Y = -21.823152843 + 22.5 Y = -21.823152843 + 22.5 Combine like terms: -21.823152843 + 22.5 = 0.676847157 Y = 0.676847157 Simplifying Y = 0.676847157Solution
The solution to the problem is based on the solutions from the subproblems. Y = {44.323152843, 0.676847157}
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