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Simplifying 5y2 = 17y + 2 Reorder the terms: 5y2 = 2 + 17y Solving 5y2 = 2 + 17y Solving for variable 'y'. Reorder the terms: -2 + -17y + 5y2 = 2 + 17y + -2 + -17y Reorder the terms: -2 + -17y + 5y2 = 2 + -2 + 17y + -17y Combine like terms: 2 + -2 = 0 -2 + -17y + 5y2 = 0 + 17y + -17y -2 + -17y + 5y2 = 17y + -17y Combine like terms: 17y + -17y = 0 -2 + -17y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -3.4y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -3.4y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -3.4y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -3.4y + y2 = 0 + 0.4 -3.4y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -3.4y + y2 = 0.4 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 = 0.4 + 2.89 Reorder the terms: 2.89 + -3.4y + y2 = 0.4 + 2.89 Combine like terms: 0.4 + 2.89 = 3.29 2.89 + -3.4y + y2 = 3.29 Factor a perfect square on the left side: (y + -1.7)(y + -1.7) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (y + -1.7) equal to 1.813835715 and -1.813835715.Subproblem 1
y + -1.7 = 1.813835715 Simplifying y + -1.7 = 1.813835715 Reorder the terms: -1.7 + y = 1.813835715 Solving -1.7 + y = 1.813835715 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 = 1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = 1.813835715 + 1.7 y = 1.813835715 + 1.7 Combine like terms: 1.813835715 + 1.7 = 3.513835715 y = 3.513835715 Simplifying y = 3.513835715Subproblem 2
y + -1.7 = -1.813835715 Simplifying y + -1.7 = -1.813835715 Reorder the terms: -1.7 + y = -1.813835715 Solving -1.7 + y = -1.813835715 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 = -1.813835715 + 1.7 Combine like terms: -1.7 + 1.7 = 0.0 0.0 + y = -1.813835715 + 1.7 y = -1.813835715 + 1.7 Combine like terms: -1.813835715 + 1.7 = -0.113835715 y = -0.113835715 Simplifying y = -0.113835715Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.513835715, -0.113835715}
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