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Simplifying 5y2 + 4y + -20 = 0 Reorder the terms: -20 + 4y + 5y2 = 0 Solving -20 + 4y + 5y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + 0.8y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.8y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 0.8y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.8y + y2 = 0 + 4 0.8y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.8y + y2 = 4 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 = 4 + 0.16 Reorder the terms: 0.16 + 0.8y + y2 = 4 + 0.16 Combine like terms: 4 + 0.16 = 4.16 0.16 + 0.8y + y2 = 4.16 Factor a perfect square on the left side: (y + 0.4)(y + 0.4) = 4.16 Calculate the square root of the right side: 2.039607805 Break this problem into two subproblems by setting (y + 0.4) equal to 2.039607805 and -2.039607805.Subproblem 1
y + 0.4 = 2.039607805 Simplifying y + 0.4 = 2.039607805 Reorder the terms: 0.4 + y = 2.039607805 Solving 0.4 + y = 2.039607805 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 = 2.039607805 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = 2.039607805 + -0.4 y = 2.039607805 + -0.4 Combine like terms: 2.039607805 + -0.4 = 1.639607805 y = 1.639607805 Simplifying y = 1.639607805Subproblem 2
y + 0.4 = -2.039607805 Simplifying y + 0.4 = -2.039607805 Reorder the terms: 0.4 + y = -2.039607805 Solving 0.4 + y = -2.039607805 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 = -2.039607805 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + y = -2.039607805 + -0.4 y = -2.039607805 + -0.4 Combine like terms: -2.039607805 + -0.4 = -2.439607805 y = -2.439607805 Simplifying y = -2.439607805Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.639607805, -2.439607805}
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