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Simplifying y2 + -62 + 2y + -5 = 180 Reorder the terms: -62 + -5 + 2y + y2 = 180 Combine like terms: -62 + -5 = -67 -67 + 2y + y2 = 180 Solving -67 + 2y + y2 = 180 Solving for variable 'y'. Reorder the terms: -67 + -180 + 2y + y2 = 180 + -180 Combine like terms: -67 + -180 = -247 -247 + 2y + y2 = 180 + -180 Combine like terms: 180 + -180 = 0 -247 + 2y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '247' to each side of the equation. -247 + 2y + 247 + y2 = 0 + 247 Reorder the terms: -247 + 247 + 2y + y2 = 0 + 247 Combine like terms: -247 + 247 = 0 0 + 2y + y2 = 0 + 247 2y + y2 = 0 + 247 Combine like terms: 0 + 247 = 247 2y + y2 = 247 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 = 247 + 1 Reorder the terms: 1 + 2y + y2 = 247 + 1 Combine like terms: 247 + 1 = 248 1 + 2y + y2 = 248 Factor a perfect square on the left side: (y + 1)(y + 1) = 248 Calculate the square root of the right side: 15.748015748 Break this problem into two subproblems by setting (y + 1) equal to 15.748015748 and -15.748015748.Subproblem 1
y + 1 = 15.748015748 Simplifying y + 1 = 15.748015748 Reorder the terms: 1 + y = 15.748015748 Solving 1 + y = 15.748015748 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 = 15.748015748 + -1 Combine like terms: 1 + -1 = 0 0 + y = 15.748015748 + -1 y = 15.748015748 + -1 Combine like terms: 15.748015748 + -1 = 14.748015748 y = 14.748015748 Simplifying y = 14.748015748Subproblem 2
y + 1 = -15.748015748 Simplifying y + 1 = -15.748015748 Reorder the terms: 1 + y = -15.748015748 Solving 1 + y = -15.748015748 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 = -15.748015748 + -1 Combine like terms: 1 + -1 = 0 0 + y = -15.748015748 + -1 y = -15.748015748 + -1 Combine like terms: -15.748015748 + -1 = -16.748015748 y = -16.748015748 Simplifying y = -16.748015748Solution
The solution to the problem is based on the solutions from the subproblems. y = {14.748015748, -16.748015748}
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