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Simplifying 28y + (y * y) + 12 = 36 Multiply y * y 28y + (y2) + 12 = 36 28y + y2 + 12 = 36 Reorder the terms: 12 + 28y + y2 = 36 Solving 12 + 28y + y2 = 36 Solving for variable 'y'. Reorder the terms: 12 + -36 + 28y + y2 = 36 + -36 Combine like terms: 12 + -36 = -24 -24 + 28y + y2 = 36 + -36 Combine like terms: 36 + -36 = 0 -24 + 28y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + 28y + 24 + y2 = 0 + 24 Reorder the terms: -24 + 24 + 28y + y2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 28y + y2 = 0 + 24 28y + y2 = 0 + 24 Combine like terms: 0 + 24 = 24 28y + y2 = 24 The y term is 28y. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28y + 196 + y2 = 24 + 196 Reorder the terms: 196 + 28y + y2 = 24 + 196 Combine like terms: 24 + 196 = 220 196 + 28y + y2 = 220 Factor a perfect square on the left side: (y + 14)(y + 14) = 220 Calculate the square root of the right side: 14.832396974 Break this problem into two subproblems by setting (y + 14) equal to 14.832396974 and -14.832396974.Subproblem 1
y + 14 = 14.832396974 Simplifying y + 14 = 14.832396974 Reorder the terms: 14 + y = 14.832396974 Solving 14 + y = 14.832396974 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = 14.832396974 + -14 Combine like terms: 14 + -14 = 0 0 + y = 14.832396974 + -14 y = 14.832396974 + -14 Combine like terms: 14.832396974 + -14 = 0.832396974 y = 0.832396974 Simplifying y = 0.832396974Subproblem 2
y + 14 = -14.832396974 Simplifying y + 14 = -14.832396974 Reorder the terms: 14 + y = -14.832396974 Solving 14 + y = -14.832396974 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + y = -14.832396974 + -14 Combine like terms: 14 + -14 = 0 0 + y = -14.832396974 + -14 y = -14.832396974 + -14 Combine like terms: -14.832396974 + -14 = -28.832396974 y = -28.832396974 Simplifying y = -28.832396974Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.832396974, -28.832396974}
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