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Simplifying 5y2 + 7y = 2 Reorder the terms: 7y + 5y2 = 2 Solving 7y + 5y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + 7y + 5y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 7y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + 1.4y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 1.4y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 1.4y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 1.4y + y2 = 0 + 0.4 1.4y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 1.4y + y2 = 0.4 The y term is 1.4y. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4y + 0.49 + y2 = 0.4 + 0.49 Reorder the terms: 0.49 + 1.4y + y2 = 0.4 + 0.49 Combine like terms: 0.4 + 0.49 = 0.89 0.49 + 1.4y + y2 = 0.89 Factor a perfect square on the left side: (y + 0.7)(y + 0.7) = 0.89 Calculate the square root of the right side: 0.943398113 Break this problem into two subproblems by setting (y + 0.7) equal to 0.943398113 and -0.943398113.Subproblem 1
y + 0.7 = 0.943398113 Simplifying y + 0.7 = 0.943398113 Reorder the terms: 0.7 + y = 0.943398113 Solving 0.7 + y = 0.943398113 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + y = 0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = 0.943398113 + -0.7 y = 0.943398113 + -0.7 Combine like terms: 0.943398113 + -0.7 = 0.243398113 y = 0.243398113 Simplifying y = 0.243398113Subproblem 2
y + 0.7 = -0.943398113 Simplifying y + 0.7 = -0.943398113 Reorder the terms: 0.7 + y = -0.943398113 Solving 0.7 + y = -0.943398113 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + y = -0.943398113 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + y = -0.943398113 + -0.7 y = -0.943398113 + -0.7 Combine like terms: -0.943398113 + -0.7 = -1.643398113 y = -1.643398113 Simplifying y = -1.643398113Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.243398113, -1.643398113}
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