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Simplifying 5y(y + -2) = 2 Reorder the terms: 5y(-2 + y) = 2 (-2 * 5y + y * 5y) = 2 (-10y + 5y2) = 2 Solving -10y + 5y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + -10y + 5y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -10y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.4 + -2y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2y + y2 = 0 + 0.4 -2y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2y + y2 = 0.4 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 0.4 + 1 Reorder the terms: 1 + -2y + y2 = 0.4 + 1 Combine like terms: 0.4 + 1 = 1.4 1 + -2y + y2 = 1.4 Factor a perfect square on the left side: (y + -1)(y + -1) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (y + -1) equal to 1.183215957 and -1.183215957.Subproblem 1
y + -1 = 1.183215957 Simplifying y + -1 = 1.183215957 Reorder the terms: -1 + y = 1.183215957 Solving -1 + y = 1.183215957 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 1.183215957 + 1 Combine like terms: -1 + 1 = 0 0 + y = 1.183215957 + 1 y = 1.183215957 + 1 Combine like terms: 1.183215957 + 1 = 2.183215957 y = 2.183215957 Simplifying y = 2.183215957Subproblem 2
y + -1 = -1.183215957 Simplifying y + -1 = -1.183215957 Reorder the terms: -1 + y = -1.183215957 Solving -1 + y = -1.183215957 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -1.183215957 + 1 Combine like terms: -1 + 1 = 0 0 + y = -1.183215957 + 1 y = -1.183215957 + 1 Combine like terms: -1.183215957 + 1 = -0.183215957 y = -0.183215957 Simplifying y = -0.183215957Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.183215957, -0.183215957}
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