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Simplifying 4y2 + -18y + 18 = 1 Reorder the terms: 18 + -18y + 4y2 = 1 Solving 18 + -18y + 4y2 = 1 Solving for variable 'y'. Reorder the terms: 18 + -1 + -18y + 4y2 = 1 + -1 Combine like terms: 18 + -1 = 17 17 + -18y + 4y2 = 1 + -1 Combine like terms: 1 + -1 = 0 17 + -18y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.25 + -4.5y + y2 = 0 Move the constant term to the right: Add '-4.25' to each side of the equation. 4.25 + -4.5y + -4.25 + y2 = 0 + -4.25 Reorder the terms: 4.25 + -4.25 + -4.5y + y2 = 0 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + -4.5y + y2 = 0 + -4.25 -4.5y + y2 = 0 + -4.25 Combine like terms: 0 + -4.25 = -4.25 -4.5y + y2 = -4.25 The y term is -4.5y. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5y + 5.0625 + y2 = -4.25 + 5.0625 Reorder the terms: 5.0625 + -4.5y + y2 = -4.25 + 5.0625 Combine like terms: -4.25 + 5.0625 = 0.8125 5.0625 + -4.5y + y2 = 0.8125 Factor a perfect square on the left side: (y + -2.25)(y + -2.25) = 0.8125 Calculate the square root of the right side: 0.901387819 Break this problem into two subproblems by setting (y + -2.25) equal to 0.901387819 and -0.901387819.Subproblem 1
y + -2.25 = 0.901387819 Simplifying y + -2.25 = 0.901387819 Reorder the terms: -2.25 + y = 0.901387819 Solving -2.25 + y = 0.901387819 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 0.901387819 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 0.901387819 + 2.25 y = 0.901387819 + 2.25 Combine like terms: 0.901387819 + 2.25 = 3.151387819 y = 3.151387819 Simplifying y = 3.151387819Subproblem 2
y + -2.25 = -0.901387819 Simplifying y + -2.25 = -0.901387819 Reorder the terms: -2.25 + y = -0.901387819 Solving -2.25 + y = -0.901387819 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -0.901387819 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -0.901387819 + 2.25 y = -0.901387819 + 2.25 Combine like terms: -0.901387819 + 2.25 = 1.348612181 y = 1.348612181 Simplifying y = 1.348612181Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.151387819, 1.348612181}
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