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Simplifying 15 + -8y + y2 = 180 Solving 15 + -8y + y2 = 180 Solving for variable 'y'. Reorder the terms: 15 + -180 + -8y + y2 = 180 + -180 Combine like terms: 15 + -180 = -165 -165 + -8y + y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -165 + -8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '165' to each side of the equation. -165 + -8y + 165 + y2 = 0 + 165 Reorder the terms: -165 + 165 + -8y + y2 = 0 + 165 Combine like terms: -165 + 165 = 0 0 + -8y + y2 = 0 + 165 -8y + y2 = 0 + 165 Combine like terms: 0 + 165 = 165 -8y + y2 = 165 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 = 165 + 16 Reorder the terms: 16 + -8y + y2 = 165 + 16 Combine like terms: 165 + 16 = 181 16 + -8y + y2 = 181 Factor a perfect square on the left side: (y + -4)(y + -4) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (y + -4) equal to 13.453624047 and -13.453624047.Subproblem 1
y + -4 = 13.453624047 Simplifying y + -4 = 13.453624047 Reorder the terms: -4 + y = 13.453624047 Solving -4 + y = 13.453624047 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 = 13.453624047 + 4 Combine like terms: -4 + 4 = 0 0 + y = 13.453624047 + 4 y = 13.453624047 + 4 Combine like terms: 13.453624047 + 4 = 17.453624047 y = 17.453624047 Simplifying y = 17.453624047Subproblem 2
y + -4 = -13.453624047 Simplifying y + -4 = -13.453624047 Reorder the terms: -4 + y = -13.453624047 Solving -4 + y = -13.453624047 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 = -13.453624047 + 4 Combine like terms: -4 + 4 = 0 0 + y = -13.453624047 + 4 y = -13.453624047 + 4 Combine like terms: -13.453624047 + 4 = -9.453624047 y = -9.453624047 Simplifying y = -9.453624047Solution
The solution to the problem is based on the solutions from the subproblems. y = {17.453624047, -9.453624047}
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