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Simplifying 5y2 + -18y + 3 = 0 Reorder the terms: 3 + -18y + 5y2 = 0 Solving 3 + -18y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + -3.6y + y2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + -3.6y + -0.6 + y2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + -3.6y + y2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + -3.6y + y2 = 0 + -0.6 -3.6y + y2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 -3.6y + y2 = -0.6 The y term is -3.6y. Take half its coefficient (-1.8). Square it (3.24) and add it to both sides. Add '3.24' to each side of the equation. -3.6y + 3.24 + y2 = -0.6 + 3.24 Reorder the terms: 3.24 + -3.6y + y2 = -0.6 + 3.24 Combine like terms: -0.6 + 3.24 = 2.64 3.24 + -3.6y + y2 = 2.64 Factor a perfect square on the left side: (y + -1.8)(y + -1.8) = 2.64 Calculate the square root of the right side: 1.624807681 Break this problem into two subproblems by setting (y + -1.8) equal to 1.624807681 and -1.624807681.Subproblem 1
y + -1.8 = 1.624807681 Simplifying y + -1.8 = 1.624807681 Reorder the terms: -1.8 + y = 1.624807681 Solving -1.8 + y = 1.624807681 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = 1.624807681 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = 1.624807681 + 1.8 y = 1.624807681 + 1.8 Combine like terms: 1.624807681 + 1.8 = 3.424807681 y = 3.424807681 Simplifying y = 3.424807681Subproblem 2
y + -1.8 = -1.624807681 Simplifying y + -1.8 = -1.624807681 Reorder the terms: -1.8 + y = -1.624807681 Solving -1.8 + y = -1.624807681 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.8' to each side of the equation. -1.8 + 1.8 + y = -1.624807681 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + y = -1.624807681 + 1.8 y = -1.624807681 + 1.8 Combine like terms: -1.624807681 + 1.8 = 0.175192319 y = 0.175192319 Simplifying y = 0.175192319Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.424807681, 0.175192319}
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