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Simplifying 48841y2 + 6187y + 187 = 0 Reorder the terms: 187 + 6187y + 48841y2 = 0 Solving 187 + 6187y + 48841y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 48841 the coefficient of the squared term: Divide each side by '48841'. 0.003828750435 + 0.126676358y + y2 = 0 Move the constant term to the right: Add '-0.003828750435' to each side of the equation. 0.003828750435 + 0.126676358y + -0.003828750435 + y2 = 0 + -0.003828750435 Reorder the terms: 0.003828750435 + -0.003828750435 + 0.126676358y + y2 = 0 + -0.003828750435 Combine like terms: 0.003828750435 + -0.003828750435 = 0.000000000000 0.000000000000 + 0.126676358y + y2 = 0 + -0.003828750435 0.126676358y + y2 = 0 + -0.003828750435 Combine like terms: 0 + -0.003828750435 = -0.003828750435 0.126676358y + y2 = -0.003828750435 The y term is 0.126676358y. Take half its coefficient (0.063338179). Square it (0.004011724919) and add it to both sides. Add '0.004011724919' to each side of the equation. 0.126676358y + 0.004011724919 + y2 = -0.003828750435 + 0.004011724919 Reorder the terms: 0.004011724919 + 0.126676358y + y2 = -0.003828750435 + 0.004011724919 Combine like terms: -0.003828750435 + 0.004011724919 = 0.000182974484 0.004011724919 + 0.126676358y + y2 = 0.000182974484 Factor a perfect square on the left side: (y + 0.063338179)(y + 0.063338179) = 0.000182974484 Calculate the square root of the right side: 0.013526806 Break this problem into two subproblems by setting (y + 0.063338179) equal to 0.013526806 and -0.013526806.Subproblem 1
y + 0.063338179 = 0.013526806 Simplifying y + 0.063338179 = 0.013526806 Reorder the terms: 0.063338179 + y = 0.013526806 Solving 0.063338179 + y = 0.013526806 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.063338179' to each side of the equation. 0.063338179 + -0.063338179 + y = 0.013526806 + -0.063338179 Combine like terms: 0.063338179 + -0.063338179 = 0.000000000 0.000000000 + y = 0.013526806 + -0.063338179 y = 0.013526806 + -0.063338179 Combine like terms: 0.013526806 + -0.063338179 = -0.049811373 y = -0.049811373 Simplifying y = -0.049811373Subproblem 2
y + 0.063338179 = -0.013526806 Simplifying y + 0.063338179 = -0.013526806 Reorder the terms: 0.063338179 + y = -0.013526806 Solving 0.063338179 + y = -0.013526806 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.063338179' to each side of the equation. 0.063338179 + -0.063338179 + y = -0.013526806 + -0.063338179 Combine like terms: 0.063338179 + -0.063338179 = 0.000000000 0.000000000 + y = -0.013526806 + -0.063338179 y = -0.013526806 + -0.063338179 Combine like terms: -0.013526806 + -0.063338179 = -0.076864985 y = -0.076864985 Simplifying y = -0.076864985Solution
The solution to the problem is based on the solutions from the subproblems. y = {-0.049811373, -0.076864985}
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