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Simplifying 5y2 + 4y = 8 Reorder the terms: 4y + 5y2 = 8 Solving 4y + 5y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + 4y + 5y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 4y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 0.8y + y2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 0.8y + 1.6 + y2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 0.8y + y2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 0.8y + y2 = 0 + 1.6 0.8y + y2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 0.8y + y2 = 1.6 The y term is 0.8y. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8y + 0.16 + y2 = 1.6 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 1.6 + 0.16 Combine like terms: 1.6 + 0.16 = 1.76 0.16 + 0.8y + y2 = 1.76 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (y + 0.4) equal to 1.326649916 and -1.326649916.Subproblem 1
y + 0.4 = 1.326649916 Simplifying y + 0.4 = 1.326649916 Reorder the terms: 0.4 + y = 1.326649916 Solving 0.4 + y = 1.326649916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = 1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 1.326649916 + -0.4 y = 1.326649916 + -0.4 Combine like terms: 1.326649916 + -0.4 = 0.926649916 y = 0.926649916 Simplifying y = 0.926649916Subproblem 2
y + 0.4 = -1.326649916 Simplifying y + 0.4 = -1.326649916 Reorder the terms: 0.4 + y = -1.326649916 Solving 0.4 + y = -1.326649916 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + y = -1.326649916 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -1.326649916 + -0.4 y = -1.326649916 + -0.4 Combine like terms: -1.326649916 + -0.4 = -1.726649916 y = -1.726649916 Simplifying y = -1.726649916Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.926649916, -1.726649916}
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