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Simplifying -26.42y + 18.6y2 = 90.8 Solving -26.42y + 18.6y2 = 90.8 Solving for variable 'y'. Reorder the terms: -90.8 + -26.42y + 18.6y2 = 90.8 + -90.8 Combine like terms: 90.8 + -90.8 = 0.0 -90.8 + -26.42y + 18.6y2 = 0.0 Begin completing the square. Divide all terms by 18.6 the coefficient of the squared term: Divide each side by '18.6'. -4.88172043 + -1.420430108y + y2 = 0 Move the constant term to the right: Add '4.88172043' to each side of the equation. -4.88172043 + -1.420430108y + 4.88172043 + y2 = 0 + 4.88172043 Reorder the terms: -4.88172043 + 4.88172043 + -1.420430108y + y2 = 0 + 4.88172043 Combine like terms: -4.88172043 + 4.88172043 = 0.00000000 0.00000000 + -1.420430108y + y2 = 0 + 4.88172043 -1.420430108y + y2 = 0 + 4.88172043 Combine like terms: 0 + 4.88172043 = 4.88172043 -1.420430108y + y2 = 4.88172043 The y term is -1.420430108y. Take half its coefficient (-0.710215054). Square it (0.5044054229) and add it to both sides. Add '0.5044054229' to each side of the equation. -1.420430108y + 0.5044054229 + y2 = 4.88172043 + 0.5044054229 Reorder the terms: 0.5044054229 + -1.420430108y + y2 = 4.88172043 + 0.5044054229 Combine like terms: 4.88172043 + 0.5044054229 = 5.3861258529 0.5044054229 + -1.420430108y + y2 = 5.3861258529 Factor a perfect square on the left side: (y + -0.710215054)(y + -0.710215054) = 5.3861258529 Calculate the square root of the right side: 2.320802847 Break this problem into two subproblems by setting (y + -0.710215054) equal to 2.320802847 and -2.320802847.Subproblem 1
y + -0.710215054 = 2.320802847 Simplifying y + -0.710215054 = 2.320802847 Reorder the terms: -0.710215054 + y = 2.320802847 Solving -0.710215054 + y = 2.320802847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.710215054' to each side of the equation. -0.710215054 + 0.710215054 + y = 2.320802847 + 0.710215054 Combine like terms: -0.710215054 + 0.710215054 = 0.000000000 0.000000000 + y = 2.320802847 + 0.710215054 y = 2.320802847 + 0.710215054 Combine like terms: 2.320802847 + 0.710215054 = 3.031017901 y = 3.031017901 Simplifying y = 3.031017901Subproblem 2
y + -0.710215054 = -2.320802847 Simplifying y + -0.710215054 = -2.320802847 Reorder the terms: -0.710215054 + y = -2.320802847 Solving -0.710215054 + y = -2.320802847 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.710215054' to each side of the equation. -0.710215054 + 0.710215054 + y = -2.320802847 + 0.710215054 Combine like terms: -0.710215054 + 0.710215054 = 0.000000000 0.000000000 + y = -2.320802847 + 0.710215054 y = -2.320802847 + 0.710215054 Combine like terms: -2.320802847 + 0.710215054 = -1.610587793 y = -1.610587793 Simplifying y = -1.610587793Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.031017901, -1.610587793}
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