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Simplifying 36y2 + -165y + 25 = 0 Reorder the terms: 25 + -165y + 36y2 = 0 Solving 25 + -165y + 36y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 0.6944444444 + -4.583333333y + y2 = 0 Move the constant term to the right: Add '-0.6944444444' to each side of the equation. 0.6944444444 + -4.583333333y + -0.6944444444 + y2 = 0 + -0.6944444444 Reorder the terms: 0.6944444444 + -0.6944444444 + -4.583333333y + y2 = 0 + -0.6944444444 Combine like terms: 0.6944444444 + -0.6944444444 = 0.0000000000 0.0000000000 + -4.583333333y + y2 = 0 + -0.6944444444 -4.583333333y + y2 = 0 + -0.6944444444 Combine like terms: 0 + -0.6944444444 = -0.6944444444 -4.583333333y + y2 = -0.6944444444 The y term is -4.583333333y. Take half its coefficient (-2.291666667). Square it (5.251736113) and add it to both sides. Add '5.251736113' to each side of the equation. -4.583333333y + 5.251736113 + y2 = -0.6944444444 + 5.251736113 Reorder the terms: 5.251736113 + -4.583333333y + y2 = -0.6944444444 + 5.251736113 Combine like terms: -0.6944444444 + 5.251736113 = 4.5572916686 5.251736113 + -4.583333333y + y2 = 4.5572916686 Factor a perfect square on the left side: (y + -2.291666667)(y + -2.291666667) = 4.5572916686 Calculate the square root of the right side: 2.13478141 Break this problem into two subproblems by setting (y + -2.291666667) equal to 2.13478141 and -2.13478141.Subproblem 1
y + -2.291666667 = 2.13478141 Simplifying y + -2.291666667 = 2.13478141 Reorder the terms: -2.291666667 + y = 2.13478141 Solving -2.291666667 + y = 2.13478141 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.291666667' to each side of the equation. -2.291666667 + 2.291666667 + y = 2.13478141 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + y = 2.13478141 + 2.291666667 y = 2.13478141 + 2.291666667 Combine like terms: 2.13478141 + 2.291666667 = 4.426448077 y = 4.426448077 Simplifying y = 4.426448077Subproblem 2
y + -2.291666667 = -2.13478141 Simplifying y + -2.291666667 = -2.13478141 Reorder the terms: -2.291666667 + y = -2.13478141 Solving -2.291666667 + y = -2.13478141 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.291666667' to each side of the equation. -2.291666667 + 2.291666667 + y = -2.13478141 + 2.291666667 Combine like terms: -2.291666667 + 2.291666667 = 0.000000000 0.000000000 + y = -2.13478141 + 2.291666667 y = -2.13478141 + 2.291666667 Combine like terms: -2.13478141 + 2.291666667 = 0.156885257 y = 0.156885257 Simplifying y = 0.156885257Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.426448077, 0.156885257}
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