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Simplifying 5y2 + 23y + 20 = 0 Reorder the terms: 20 + 23y + 5y2 = 0 Solving 20 + 23y + 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 + 4.6y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + 4.6y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + 4.6y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 4.6y + y2 = 0 + -4 4.6y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 4.6y + y2 = -4 The y term is 4.6y. Take half its coefficient (2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. 4.6y + 5.29 + y2 = -4 + 5.29 Reorder the terms: 5.29 + 4.6y + y2 = -4 + 5.29 Combine like terms: -4 + 5.29 = 1.29 5.29 + 4.6y + y2 = 1.29 Factor a perfect square on the left side: (y + 2.3)(y + 2.3) = 1.29 Calculate the square root of the right side: 1.135781669 Break this problem into two subproblems by setting (y + 2.3) equal to 1.135781669 and -1.135781669.Subproblem 1
y + 2.3 = 1.135781669 Simplifying y + 2.3 = 1.135781669 Reorder the terms: 2.3 + y = 1.135781669 Solving 2.3 + y = 1.135781669 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + y = 1.135781669 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + y = 1.135781669 + -2.3 y = 1.135781669 + -2.3 Combine like terms: 1.135781669 + -2.3 = -1.164218331 y = -1.164218331 Simplifying y = -1.164218331Subproblem 2
y + 2.3 = -1.135781669 Simplifying y + 2.3 = -1.135781669 Reorder the terms: 2.3 + y = -1.135781669 Solving 2.3 + y = -1.135781669 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.3' to each side of the equation. 2.3 + -2.3 + y = -1.135781669 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + y = -1.135781669 + -2.3 y = -1.135781669 + -2.3 Combine like terms: -1.135781669 + -2.3 = -3.435781669 y = -3.435781669 Simplifying y = -3.435781669Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.164218331, -3.435781669}
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