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Simplifying 2y + 5y(2 + -1y) = 3 + -5 2y + (2 * 5y + -1y * 5y) = 3 + -5 2y + (10y + -5y2) = 3 + -5 Combine like terms: 2y + 10y = 12y 12y + -5y2 = 3 + -5 Combine like terms: 3 + -5 = -2 12y + -5y2 = -2 Solving 12y + -5y2 = -2 Solving for variable 'y'. Reorder the terms: 2 + 12y + -5y2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 12y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.4 + -2.4y + y2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + -2.4y + 0.4 + y2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + -2.4y + y2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + -2.4y + y2 = 0 + 0.4 -2.4y + y2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 -2.4y + y2 = 0.4 The y term is -2.4y. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4y + 1.44 + y2 = 0.4 + 1.44 Reorder the terms: 1.44 + -2.4y + y2 = 0.4 + 1.44 Combine like terms: 0.4 + 1.44 = 1.84 1.44 + -2.4y + y2 = 1.84 Factor a perfect square on the left side: (y + -1.2)(y + -1.2) = 1.84 Calculate the square root of the right side: 1.356465997 Break this problem into two subproblems by setting (y + -1.2) equal to 1.356465997 and -1.356465997.Subproblem 1
y + -1.2 = 1.356465997 Simplifying y + -1.2 = 1.356465997 Reorder the terms: -1.2 + y = 1.356465997 Solving -1.2 + y = 1.356465997 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + y = 1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = 1.356465997 + 1.2 y = 1.356465997 + 1.2 Combine like terms: 1.356465997 + 1.2 = 2.556465997 y = 2.556465997 Simplifying y = 2.556465997Subproblem 2
y + -1.2 = -1.356465997 Simplifying y + -1.2 = -1.356465997 Reorder the terms: -1.2 + y = -1.356465997 Solving -1.2 + y = -1.356465997 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + y = -1.356465997 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + y = -1.356465997 + 1.2 y = -1.356465997 + 1.2 Combine like terms: -1.356465997 + 1.2 = -0.156465997 y = -0.156465997 Simplifying y = -0.156465997Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.556465997, -0.156465997}
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