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Simplifying y2 + -2y = 90 Reorder the terms: -2y + y2 = 90 Solving -2y + y2 = 90 Solving for variable 'y'. Reorder the terms: -90 + -2y + y2 = 90 + -90 Combine like terms: 90 + -90 = 0 -90 + -2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + -2y + 90 + y2 = 0 + 90 Reorder the terms: -90 + 90 + -2y + y2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -2y + y2 = 0 + 90 -2y + y2 = 0 + 90 Combine like terms: 0 + 90 = 90 -2y + y2 = 90 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 90 + 1 Reorder the terms: 1 + -2y + y2 = 90 + 1 Combine like terms: 90 + 1 = 91 1 + -2y + y2 = 91 Factor a perfect square on the left side: (y + -1)(y + -1) = 91 Calculate the square root of the right side: 9.539392014 Break this problem into two subproblems by setting (y + -1) equal to 9.539392014 and -9.539392014.Subproblem 1
y + -1 = 9.539392014 Simplifying y + -1 = 9.539392014 Reorder the terms: -1 + y = 9.539392014 Solving -1 + y = 9.539392014 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + y = 9.539392014 + 1 y = 9.539392014 + 1 Combine like terms: 9.539392014 + 1 = 10.539392014 y = 10.539392014 Simplifying y = 10.539392014Subproblem 2
y + -1 = -9.539392014 Simplifying y + -1 = -9.539392014 Reorder the terms: -1 + y = -9.539392014 Solving -1 + y = -9.539392014 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -9.539392014 + 1 Combine like terms: -1 + 1 = 0 0 + y = -9.539392014 + 1 y = -9.539392014 + 1 Combine like terms: -9.539392014 + 1 = -8.539392014 y = -8.539392014 Simplifying y = -8.539392014Solution
The solution to the problem is based on the solutions from the subproblems. y = {10.539392014, -8.539392014}
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