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Simplifying Y2 + -35 = 15Y Reorder the terms: -35 + Y2 = 15Y Solving -35 + Y2 = 15Y Solving for variable 'Y'. Reorder the terms: -35 + -15Y + Y2 = 15Y + -15Y Combine like terms: 15Y + -15Y = 0 -35 + -15Y + Y2 = 0 Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + -15Y + 35 + Y2 = 0 + 35 Reorder the terms: -35 + 35 + -15Y + Y2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -15Y + Y2 = 0 + 35 -15Y + Y2 = 0 + 35 Combine like terms: 0 + 35 = 35 -15Y + Y2 = 35 The Y term is -15Y. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15Y + 56.25 + Y2 = 35 + 56.25 Reorder the terms: 56.25 + -15Y + Y2 = 35 + 56.25 Combine like terms: 35 + 56.25 = 91.25 56.25 + -15Y + Y2 = 91.25 Factor a perfect square on the left side: (Y + -7.5)(Y + -7.5) = 91.25 Calculate the square root of the right side: 9.552486587 Break this problem into two subproblems by setting (Y + -7.5) equal to 9.552486587 and -9.552486587.Subproblem 1
Y + -7.5 = 9.552486587 Simplifying Y + -7.5 = 9.552486587 Reorder the terms: -7.5 + Y = 9.552486587 Solving -7.5 + Y = 9.552486587 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + Y = 9.552486587 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + Y = 9.552486587 + 7.5 Y = 9.552486587 + 7.5 Combine like terms: 9.552486587 + 7.5 = 17.052486587 Y = 17.052486587 Simplifying Y = 17.052486587Subproblem 2
Y + -7.5 = -9.552486587 Simplifying Y + -7.5 = -9.552486587 Reorder the terms: -7.5 + Y = -9.552486587 Solving -7.5 + Y = -9.552486587 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + Y = -9.552486587 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + Y = -9.552486587 + 7.5 Y = -9.552486587 + 7.5 Combine like terms: -9.552486587 + 7.5 = -2.052486587 Y = -2.052486587 Simplifying Y = -2.052486587Solution
The solution to the problem is based on the solutions from the subproblems. Y = {17.052486587, -2.052486587}
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