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Simplifying y2 + -72y + 12 = 0 Reorder the terms: 12 + -72y + y2 = 0 Solving 12 + -72y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -72y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -72y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -72y + y2 = 0 + -12 -72y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -72y + y2 = -12 The y term is -72y. Take half its coefficient (-36). Square it (1296) and add it to both sides. Add '1296' to each side of the equation. -72y + 1296 + y2 = -12 + 1296 Reorder the terms: 1296 + -72y + y2 = -12 + 1296 Combine like terms: -12 + 1296 = 1284 1296 + -72y + y2 = 1284 Factor a perfect square on the left side: (y + -36)(y + -36) = 1284 Calculate the square root of the right side: 35.832945734 Break this problem into two subproblems by setting (y + -36) equal to 35.832945734 and -35.832945734.Subproblem 1
y + -36 = 35.832945734 Simplifying y + -36 = 35.832945734 Reorder the terms: -36 + y = 35.832945734 Solving -36 + y = 35.832945734 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + y = 35.832945734 + 36 Combine like terms: -36 + 36 = 0 0 + y = 35.832945734 + 36 y = 35.832945734 + 36 Combine like terms: 35.832945734 + 36 = 71.832945734 y = 71.832945734 Simplifying y = 71.832945734Subproblem 2
y + -36 = -35.832945734 Simplifying y + -36 = -35.832945734 Reorder the terms: -36 + y = -35.832945734 Solving -36 + y = -35.832945734 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '36' to each side of the equation. -36 + 36 + y = -35.832945734 + 36 Combine like terms: -36 + 36 = 0 0 + y = -35.832945734 + 36 y = -35.832945734 + 36 Combine like terms: -35.832945734 + 36 = 0.167054266 y = 0.167054266 Simplifying y = 0.167054266Solution
The solution to the problem is based on the solutions from the subproblems. y = {71.832945734, 0.167054266}
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