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Simplifying (y2 + -86y + 45) = 0 Reorder the terms: (45 + -86y + y2) = 0 Remove parenthesis around (45 + -86y + y2) 45 + -86y + y2 = 0 Solving 45 + -86y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -86y + -45 + y2 = 0 + -45 Reorder the terms: 45 + -45 + -86y + y2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -86y + y2 = 0 + -45 -86y + y2 = 0 + -45 Combine like terms: 0 + -45 = -45 -86y + y2 = -45 The y term is -86y. Take half its coefficient (-43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. -86y + 1849 + y2 = -45 + 1849 Reorder the terms: 1849 + -86y + y2 = -45 + 1849 Combine like terms: -45 + 1849 = 1804 1849 + -86y + y2 = 1804 Factor a perfect square on the left side: (y + -43)(y + -43) = 1804 Calculate the square root of the right side: 42.473521163 Break this problem into two subproblems by setting (y + -43) equal to 42.473521163 and -42.473521163.Subproblem 1
y + -43 = 42.473521163 Simplifying y + -43 = 42.473521163 Reorder the terms: -43 + y = 42.473521163 Solving -43 + y = 42.473521163 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + y = 42.473521163 + 43 Combine like terms: -43 + 43 = 0 0 + y = 42.473521163 + 43 y = 42.473521163 + 43 Combine like terms: 42.473521163 + 43 = 85.473521163 y = 85.473521163 Simplifying y = 85.473521163Subproblem 2
y + -43 = -42.473521163 Simplifying y + -43 = -42.473521163 Reorder the terms: -43 + y = -42.473521163 Solving -43 + y = -42.473521163 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + y = -42.473521163 + 43 Combine like terms: -43 + 43 = 0 0 + y = -42.473521163 + 43 y = -42.473521163 + 43 Combine like terms: -42.473521163 + 43 = 0.526478837 y = 0.526478837 Simplifying y = 0.526478837Solution
The solution to the problem is based on the solutions from the subproblems. y = {85.473521163, 0.526478837}
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