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Simplifying y(y) + -36y + 160 = 0 Multiply y * y y2 + -36y + 160 = 0 Reorder the terms: 160 + -36y + y2 = 0 Solving 160 + -36y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-160' to each side of the equation. 160 + -36y + -160 + y2 = 0 + -160 Reorder the terms: 160 + -160 + -36y + y2 = 0 + -160 Combine like terms: 160 + -160 = 0 0 + -36y + y2 = 0 + -160 -36y + y2 = 0 + -160 Combine like terms: 0 + -160 = -160 -36y + y2 = -160 The y term is -36y. Take half its coefficient (-18). Square it (324) and add it to both sides. Add '324' to each side of the equation. -36y + 324 + y2 = -160 + 324 Reorder the terms: 324 + -36y + y2 = -160 + 324 Combine like terms: -160 + 324 = 164 324 + -36y + y2 = 164 Factor a perfect square on the left side: (y + -18)(y + -18) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (y + -18) equal to 12.806248475 and -12.806248475.Subproblem 1
y + -18 = 12.806248475 Simplifying y + -18 = 12.806248475 Reorder the terms: -18 + y = 12.806248475 Solving -18 + y = 12.806248475 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = 12.806248475 + 18 Combine like terms: -18 + 18 = 0 0 + y = 12.806248475 + 18 y = 12.806248475 + 18 Combine like terms: 12.806248475 + 18 = 30.806248475 y = 30.806248475 Simplifying y = 30.806248475Subproblem 2
y + -18 = -12.806248475 Simplifying y + -18 = -12.806248475 Reorder the terms: -18 + y = -12.806248475 Solving -18 + y = -12.806248475 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + y = -12.806248475 + 18 Combine like terms: -18 + 18 = 0 0 + y = -12.806248475 + 18 y = -12.806248475 + 18 Combine like terms: -12.806248475 + 18 = 5.193751525 y = 5.193751525 Simplifying y = 5.193751525Solution
The solution to the problem is based on the solutions from the subproblems. y = {30.806248475, 5.193751525}
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