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Simplifying 5y2 + 23y + 10 = 0 Reorder the terms: 10 + 23y + 5y2 = 0 Solving 10 + 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'. 2 + 4.6y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 4.6y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + 4.6y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 4.6y + y2 = 0 + -2 4.6y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 4.6y + y2 = -2 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 = -2 + 5.29 Reorder the terms: 5.29 + 4.6y + y2 = -2 + 5.29 Combine like terms: -2 + 5.29 = 3.29 5.29 + 4.6y + y2 = 3.29 Factor a perfect square on the left side: (y + 2.3)(y + 2.3) = 3.29 Calculate the square root of the right side: 1.813835715 Break this problem into two subproblems by setting (y + 2.3) equal to 1.813835715 and -1.813835715.Subproblem 1
y + 2.3 = 1.813835715 Simplifying y + 2.3 = 1.813835715 Reorder the terms: 2.3 + y = 1.813835715 Solving 2.3 + y = 1.813835715 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 = 1.813835715 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + y = 1.813835715 + -2.3 y = 1.813835715 + -2.3 Combine like terms: 1.813835715 + -2.3 = -0.486164285 y = -0.486164285 Simplifying y = -0.486164285Subproblem 2
y + 2.3 = -1.813835715 Simplifying y + 2.3 = -1.813835715 Reorder the terms: 2.3 + y = -1.813835715 Solving 2.3 + y = -1.813835715 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 = -1.813835715 + -2.3 Combine like terms: 2.3 + -2.3 = 0.0 0.0 + y = -1.813835715 + -2.3 y = -1.813835715 + -2.3 Combine like terms: -1.813835715 + -2.3 = -4.113835715 y = -4.113835715 Simplifying y = -4.113835715Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.486164285, -4.113835715}
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