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Simplifying y2 + -20y + 25 = 32 Reorder the terms: 25 + -20y + y2 = 32 Solving 25 + -20y + y2 = 32 Solving for variable 'y'. Reorder the terms: 25 + -32 + -20y + y2 = 32 + -32 Combine like terms: 25 + -32 = -7 -7 + -20y + y2 = 32 + -32 Combine like terms: 32 + -32 = 0 -7 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -20y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -20y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -20y + y2 = 0 + 7 -20y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -20y + y2 = 7 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = 7 + 100 Reorder the terms: 100 + -20y + y2 = 7 + 100 Combine like terms: 7 + 100 = 107 100 + -20y + y2 = 107 Factor a perfect square on the left side: (y + -10)(y + -10) = 107 Calculate the square root of the right side: 10.344080433 Break this problem into two subproblems by setting (y + -10) equal to 10.344080433 and -10.344080433.Subproblem 1
y + -10 = 10.344080433 Simplifying y + -10 = 10.344080433 Reorder the terms: -10 + y = 10.344080433 Solving -10 + y = 10.344080433 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 10.344080433 + 10 Combine like terms: -10 + 10 = 0 0 + y = 10.344080433 + 10 y = 10.344080433 + 10 Combine like terms: 10.344080433 + 10 = 20.344080433 y = 20.344080433 Simplifying y = 20.344080433Subproblem 2
y + -10 = -10.344080433 Simplifying y + -10 = -10.344080433 Reorder the terms: -10 + y = -10.344080433 Solving -10 + y = -10.344080433 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -10.344080433 + 10 Combine like terms: -10 + 10 = 0 0 + y = -10.344080433 + 10 y = -10.344080433 + 10 Combine like terms: -10.344080433 + 10 = -0.344080433 y = -0.344080433 Simplifying y = -0.344080433Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.344080433, -0.344080433}
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