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Simplifying 5y + -4y(2y + -4y) = 2 Combine like terms: 2y + -4y = -2y 5y + -4y(-2y) = 2 Remove parenthesis around (-2y) 5y + -4y * -2y = 2 Reorder the terms for easier multiplication: 5y + -4 * -2y * y = 2 Multiply -4 * -2 5y + 8y * y = 2 Multiply y * y 5y + 8y2 = 2 Solving 5y + 8y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + 5y + 8y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + 5y + 8y2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.25 + 0.625y + y2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + 0.625y + 0.25 + y2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + 0.625y + y2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + 0.625y + y2 = 0 + 0.25 0.625y + y2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 0.625y + y2 = 0.25 The y term is 0.625y. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625y + 0.09765625 + y2 = 0.25 + 0.09765625 Reorder the terms: 0.09765625 + 0.625y + y2 = 0.25 + 0.09765625 Combine like terms: 0.25 + 0.09765625 = 0.34765625 0.09765625 + 0.625y + y2 = 0.34765625 Factor a perfect square on the left side: (y + 0.3125)(y + 0.3125) = 0.34765625 Calculate the square root of the right side: 0.589623821 Break this problem into two subproblems by setting (y + 0.3125) equal to 0.589623821 and -0.589623821.Subproblem 1
y + 0.3125 = 0.589623821 Simplifying y + 0.3125 = 0.589623821 Reorder the terms: 0.3125 + y = 0.589623821 Solving 0.3125 + y = 0.589623821 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + y = 0.589623821 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + y = 0.589623821 + -0.3125 y = 0.589623821 + -0.3125 Combine like terms: 0.589623821 + -0.3125 = 0.277123821 y = 0.277123821 Simplifying y = 0.277123821Subproblem 2
y + 0.3125 = -0.589623821 Simplifying y + 0.3125 = -0.589623821 Reorder the terms: 0.3125 + y = -0.589623821 Solving 0.3125 + y = -0.589623821 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + y = -0.589623821 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + y = -0.589623821 + -0.3125 y = -0.589623821 + -0.3125 Combine like terms: -0.589623821 + -0.3125 = -0.902123821 y = -0.902123821 Simplifying y = -0.902123821Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.277123821, -0.902123821}
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