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Simplifying 5y2 + -17y + 4 = 0 Reorder the terms: 4 + -17y + 5y2 = 0 Solving 4 + -17y + 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'. 0.8 + -3.4y + y2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + -3.4y + -0.8 + y2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + -3.4y + y2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + -3.4y + y2 = 0 + -0.8 -3.4y + y2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 -3.4y + y2 = -0.8 The y term is -3.4y. Take half its coefficient (-1.7). Square it (2.89) and add it to both sides. Add '2.89' to each side of the equation. -3.4y + 2.89 + y2 = -0.8 + 2.89 Reorder the terms: 2.89 + -3.4y + y2 = -0.8 + 2.89 Combine like terms: -0.8 + 2.89 = 2.09 2.89 + -3.4y + y2 = 2.09 Factor a perfect square on the left side: (y + -1.7)(y + -1.7) = 2.09 Calculate the square root of the right side: 1.445683229 Break this problem into two subproblems by setting (y + -1.7) equal to 1.445683229 and -1.445683229.Subproblem 1
y + -1.7 = 1.445683229 Simplifying y + -1.7 = 1.445683229 Reorder the terms: -1.7 + y = 1.445683229 Solving -1.7 + y = 1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + y = 1.445683229 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = 1.445683229 + 1.7 y = 1.445683229 + 1.7 Combine like terms: 1.445683229 + 1.7 = 3.145683229 y = 3.145683229 Simplifying y = 3.145683229Subproblem 2
y + -1.7 = -1.445683229 Simplifying y + -1.7 = -1.445683229 Reorder the terms: -1.7 + y = -1.445683229 Solving -1.7 + y = -1.445683229 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.7' to each side of the equation. -1.7 + 1.7 + y = -1.445683229 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = -1.445683229 + 1.7 y = -1.445683229 + 1.7 Combine like terms: -1.445683229 + 1.7 = 0.254316771 y = 0.254316771 Simplifying y = 0.254316771Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.145683229, 0.254316771}
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