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Simplifying 5y2 + 8y = 8 Reorder the terms: 8y + 5y2 = 8 Solving 8y + 5y2 = 8 Solving for variable 'y'. Reorder the terms: -8 + 8y + 5y2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + 8y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.6 + 1.6y + y2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 1.6y + 1.6 + y2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 1.6y + y2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 1.6y + y2 = 0 + 1.6 1.6y + y2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 1.6y + y2 = 1.6 The y term is 1.6y. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6y + 0.64 + y2 = 1.6 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = 1.6 + 0.64 Combine like terms: 1.6 + 0.64 = 2.24 0.64 + 1.6y + y2 = 2.24 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = 2.24 Calculate the square root of the right side: 1.496662955 Break this problem into two subproblems by setting (y + 0.8) equal to 1.496662955 and -1.496662955.Subproblem 1
y + 0.8 = 1.496662955 Simplifying y + 0.8 = 1.496662955 Reorder the terms: 0.8 + y = 1.496662955 Solving 0.8 + y = 1.496662955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + y = 1.496662955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = 1.496662955 + -0.8 y = 1.496662955 + -0.8 Combine like terms: 1.496662955 + -0.8 = 0.696662955 y = 0.696662955 Simplifying y = 0.696662955Subproblem 2
y + 0.8 = -1.496662955 Simplifying y + 0.8 = -1.496662955 Reorder the terms: 0.8 + y = -1.496662955 Solving 0.8 + y = -1.496662955 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + y = -1.496662955 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + y = -1.496662955 + -0.8 y = -1.496662955 + -0.8 Combine like terms: -1.496662955 + -0.8 = -2.296662955 y = -2.296662955 Simplifying y = -2.296662955Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.696662955, -2.296662955}
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