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Simplifying y2 + -18y + 64 = 0 Reorder the terms: 64 + -18y + y2 = 0 Solving 64 + -18y + 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 + -18y + -64 + y2 = 0 + -64 Reorder the terms: 64 + -64 + -18y + y2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -18y + y2 = 0 + -64 -18y + y2 = 0 + -64 Combine like terms: 0 + -64 = -64 -18y + y2 = -64 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 = -64 + 81 Reorder the terms: 81 + -18y + y2 = -64 + 81 Combine like terms: -64 + 81 = 17 81 + -18y + y2 = 17 Factor a perfect square on the left side: (y + -9)(y + -9) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -9) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -9 = 4.123105626 Simplifying y + -9 = 4.123105626 Reorder the terms: -9 + y = 4.123105626 Solving -9 + y = 4.123105626 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 = 4.123105626 + 9 Combine like terms: -9 + 9 = 0 0 + y = 4.123105626 + 9 y = 4.123105626 + 9 Combine like terms: 4.123105626 + 9 = 13.123105626 y = 13.123105626 Simplifying y = 13.123105626Subproblem 2
y + -9 = -4.123105626 Simplifying y + -9 = -4.123105626 Reorder the terms: -9 + y = -4.123105626 Solving -9 + y = -4.123105626 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 = -4.123105626 + 9 Combine like terms: -9 + 9 = 0 0 + y = -4.123105626 + 9 y = -4.123105626 + 9 Combine like terms: -4.123105626 + 9 = 4.876894374 y = 4.876894374 Simplifying y = 4.876894374Solution
The solution to the problem is based on the solutions from the subproblems. y = {13.123105626, 4.876894374}
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