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Simplifying 0 = y2 + -8y + -160 Reorder the terms: 0 = -160 + -8y + y2 Solving 0 = -160 + -8y + y2 Solving for variable 'y'. Combine like terms: 0 + 160 = 160 160 + 8y + -1y2 = -160 + -8y + y2 + 160 + 8y + -1y2 Reorder the terms: 160 + 8y + -1y2 = -160 + 160 + -8y + 8y + y2 + -1y2 Combine like terms: -160 + 160 = 0 160 + 8y + -1y2 = 0 + -8y + 8y + y2 + -1y2 160 + 8y + -1y2 = -8y + 8y + y2 + -1y2 Combine like terms: -8y + 8y = 0 160 + 8y + -1y2 = 0 + y2 + -1y2 160 + 8y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 160 + 8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -160 + -8y + y2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -8y + 160 + y2 = 0 + 160 Reorder the terms: -160 + 160 + -8y + y2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -8y + y2 = 0 + 160 -8y + y2 = 0 + 160 Combine like terms: 0 + 160 = 160 -8y + y2 = 160 The y term is -8y. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8y + 16 + y2 = 160 + 16 Reorder the terms: 16 + -8y + y2 = 160 + 16 Combine like terms: 160 + 16 = 176 16 + -8y + y2 = 176 Factor a perfect square on the left side: (y + -4)(y + -4) = 176 Calculate the square root of the right side: 13.266499161 Break this problem into two subproblems by setting (y + -4) equal to 13.266499161 and -13.266499161.Subproblem 1
y + -4 = 13.266499161 Simplifying y + -4 = 13.266499161 Reorder the terms: -4 + y = 13.266499161 Solving -4 + y = 13.266499161 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = 13.266499161 + 4 Combine like terms: -4 + 4 = 0 0 + y = 13.266499161 + 4 y = 13.266499161 + 4 Combine like terms: 13.266499161 + 4 = 17.266499161 y = 17.266499161 Simplifying y = 17.266499161Subproblem 2
y + -4 = -13.266499161 Simplifying y + -4 = -13.266499161 Reorder the terms: -4 + y = -13.266499161 Solving -4 + y = -13.266499161 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + y = -13.266499161 + 4 Combine like terms: -4 + 4 = 0 0 + y = -13.266499161 + 4 y = -13.266499161 + 4 Combine like terms: -13.266499161 + 4 = -9.266499161 y = -9.266499161 Simplifying y = -9.266499161Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.266499161, -9.266499161}
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