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Simplifying 25y2 + 30y + 2 = 0 Reorder the terms: 2 + 30y + 25y2 = 0 Solving 2 + 30y + 25y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.08 + 1.2y + y2 = 0 Move the constant term to the right: Add '-0.08' to each side of the equation. 0.08 + 1.2y + -0.08 + y2 = 0 + -0.08 Reorder the terms: 0.08 + -0.08 + 1.2y + y2 = 0 + -0.08 Combine like terms: 0.08 + -0.08 = 0.00 0.00 + 1.2y + y2 = 0 + -0.08 1.2y + y2 = 0 + -0.08 Combine like terms: 0 + -0.08 = -0.08 1.2y + y2 = -0.08 The y term is 1.2y. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2y + 0.36 + y2 = -0.08 + 0.36 Reorder the terms: 0.36 + 1.2y + y2 = -0.08 + 0.36 Combine like terms: -0.08 + 0.36 = 0.28 0.36 + 1.2y + y2 = 0.28 Factor a perfect square on the left side: (y + 0.6)(y + 0.6) = 0.28 Calculate the square root of the right side: 0.529150262 Break this problem into two subproblems by setting (y + 0.6) equal to 0.529150262 and -0.529150262.Subproblem 1
y + 0.6 = 0.529150262 Simplifying y + 0.6 = 0.529150262 Reorder the terms: 0.6 + y = 0.529150262 Solving 0.6 + y = 0.529150262 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = 0.529150262 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = 0.529150262 + -0.6 y = 0.529150262 + -0.6 Combine like terms: 0.529150262 + -0.6 = -0.070849738 y = -0.070849738 Simplifying y = -0.070849738Subproblem 2
y + 0.6 = -0.529150262 Simplifying y + 0.6 = -0.529150262 Reorder the terms: 0.6 + y = -0.529150262 Solving 0.6 + y = -0.529150262 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + y = -0.529150262 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + y = -0.529150262 + -0.6 y = -0.529150262 + -0.6 Combine like terms: -0.529150262 + -0.6 = -1.129150262 y = -1.129150262 Simplifying y = -1.129150262Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.070849738, -1.129150262}
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