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Simplifying 5y2 + 2y + -20 = 0 Reorder the terms: -20 + 2y + 5y2 = 0 Solving -20 + 2y + 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 + 0.4y + y2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + 0.4y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + 0.4y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 0.4y + y2 = 0 + 4 0.4y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 0.4y + y2 = 4 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 4 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 4 + 0.04 Combine like terms: 4 + 0.04 = 4.04 0.04 + 0.4y + y2 = 4.04 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 4.04 Calculate the square root of the right side: 2.009975124 Break this problem into two subproblems by setting (y + 0.2) equal to 2.009975124 and -2.009975124.Subproblem 1
y + 0.2 = 2.009975124 Simplifying y + 0.2 = 2.009975124 Reorder the terms: 0.2 + y = 2.009975124 Solving 0.2 + y = 2.009975124 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 2.009975124 + -0.2 y = 2.009975124 + -0.2 Combine like terms: 2.009975124 + -0.2 = 1.809975124 y = 1.809975124 Simplifying y = 1.809975124Subproblem 2
y + 0.2 = -2.009975124 Simplifying y + 0.2 = -2.009975124 Reorder the terms: 0.2 + y = -2.009975124 Solving 0.2 + y = -2.009975124 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -2.009975124 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -2.009975124 + -0.2 y = -2.009975124 + -0.2 Combine like terms: -2.009975124 + -0.2 = -2.209975124 y = -2.209975124 Simplifying y = -2.209975124Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.809975124, -2.209975124}
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