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Simplifying y2 + -18y + -34 = 0 Reorder the terms: -34 + -18y + y2 = 0 Solving -34 + -18y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -18y + 34 + y2 = 0 + 34 Reorder the terms: -34 + 34 + -18y + y2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -18y + y2 = 0 + 34 -18y + y2 = 0 + 34 Combine like terms: 0 + 34 = 34 -18y + y2 = 34 The y term is -18y. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18y + 81 + y2 = 34 + 81 Reorder the terms: 81 + -18y + y2 = 34 + 81 Combine like terms: 34 + 81 = 115 81 + -18y + y2 = 115 Factor a perfect square on the left side: (y + -9)(y + -9) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (y + -9) equal to 10.723805295 and -10.723805295.Subproblem 1
y + -9 = 10.723805295 Simplifying y + -9 = 10.723805295 Reorder the terms: -9 + y = 10.723805295 Solving -9 + y = 10.723805295 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = 10.723805295 + 9 Combine like terms: -9 + 9 = 0 0 + y = 10.723805295 + 9 y = 10.723805295 + 9 Combine like terms: 10.723805295 + 9 = 19.723805295 y = 19.723805295 Simplifying y = 19.723805295Subproblem 2
y + -9 = -10.723805295 Simplifying y + -9 = -10.723805295 Reorder the terms: -9 + y = -10.723805295 Solving -9 + y = -10.723805295 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + y = -10.723805295 + 9 Combine like terms: -9 + 9 = 0 0 + y = -10.723805295 + 9 y = -10.723805295 + 9 Combine like terms: -10.723805295 + 9 = -1.723805295 y = -1.723805295 Simplifying y = -1.723805295Solution
The solution to the problem is based on the solutions from the subproblems. y = {19.723805295, -1.723805295}
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