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Simplifying y2 + 8y + -15 = 180 Reorder the terms: -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 = -195 -195 + 8y + y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -195 + 8y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '195' to each side of the equation. -195 + 8y + 195 + y2 = 0 + 195 Reorder the terms: -195 + 195 + 8y + y2 = 0 + 195 Combine like terms: -195 + 195 = 0 0 + 8y + y2 = 0 + 195 8y + y2 = 0 + 195 Combine like terms: 0 + 195 = 195 8y + y2 = 195 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 = 195 + 16 Reorder the terms: 16 + 8y + y2 = 195 + 16 Combine like terms: 195 + 16 = 211 16 + 8y + y2 = 211 Factor a perfect square on the left side: (y + 4)(y + 4) = 211 Calculate the square root of the right side: 14.525839046 Break this problem into two subproblems by setting (y + 4) equal to 14.525839046 and -14.525839046.Subproblem 1
y + 4 = 14.525839046 Simplifying y + 4 = 14.525839046 Reorder the terms: 4 + y = 14.525839046 Solving 4 + y = 14.525839046 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 = 14.525839046 + -4 Combine like terms: 4 + -4 = 0 0 + y = 14.525839046 + -4 y = 14.525839046 + -4 Combine like terms: 14.525839046 + -4 = 10.525839046 y = 10.525839046 Simplifying y = 10.525839046Subproblem 2
y + 4 = -14.525839046 Simplifying y + 4 = -14.525839046 Reorder the terms: 4 + y = -14.525839046 Solving 4 + y = -14.525839046 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 = -14.525839046 + -4 Combine like terms: 4 + -4 = 0 0 + y = -14.525839046 + -4 y = -14.525839046 + -4 Combine like terms: -14.525839046 + -4 = -18.525839046 y = -18.525839046 Simplifying y = -18.525839046Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.525839046, -18.525839046}
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