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Simplifying 4y2 + -1(4 + -2y + -2y + -1y2) = 11 Combine like terms: -2y + -2y = -4y 4y2 + -1(4 + -4y + -1y2) = 11 4y2 + (4 * -1 + -4y * -1 + -1y2 * -1) = 11 4y2 + (-4 + 4y + 1y2) = 11 Reorder the terms: -4 + 4y + 4y2 + 1y2 = 11 Combine like terms: 4y2 + 1y2 = 5y2 -4 + 4y + 5y2 = 11 Solving -4 + 4y + 5y2 = 11 Solving for variable 'y'. Reorder the terms: -4 + -11 + 4y + 5y2 = 11 + -11 Combine like terms: -4 + -11 = -15 -15 + 4y + 5y2 = 11 + -11 Combine like terms: 11 + -11 = 0 -15 + 4y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3 + 0.8y + y2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 0.8y + 3 + y2 = 0 + 3 Reorder the terms: -3 + 3 + 0.8y + y2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 0.8y + y2 = 0 + 3 0.8y + y2 = 0 + 3 Combine like terms: 0 + 3 = 3 0.8y + y2 = 3 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 = 3 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 3 + 0.16 Combine like terms: 3 + 0.16 = 3.16 0.16 + 0.8y + y2 = 3.16 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 3.16 Calculate the square root of the right side: 1.777638883 Break this problem into two subproblems by setting (y + 0.4) equal to 1.777638883 and -1.777638883.Subproblem 1
y + 0.4 = 1.777638883 Simplifying y + 0.4 = 1.777638883 Reorder the terms: 0.4 + y = 1.777638883 Solving 0.4 + y = 1.777638883 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 = 1.777638883 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 1.777638883 + -0.4 y = 1.777638883 + -0.4 Combine like terms: 1.777638883 + -0.4 = 1.377638883 y = 1.377638883 Simplifying y = 1.377638883Subproblem 2
y + 0.4 = -1.777638883 Simplifying y + 0.4 = -1.777638883 Reorder the terms: 0.4 + y = -1.777638883 Solving 0.4 + y = -1.777638883 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 = -1.777638883 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -1.777638883 + -0.4 y = -1.777638883 + -0.4 Combine like terms: -1.777638883 + -0.4 = -2.177638883 y = -2.177638883 Simplifying y = -2.177638883Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.377638883, -2.177638883}
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