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Simplifying 2y2 + -4.95y + -3.04 = 0 Reorder the terms: -3.04 + -4.95y + 2y2 = 0 Solving -3.04 + -4.95y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.52 + -2.475y + y2 = 0 Move the constant term to the right: Add '1.52' to each side of the equation. -1.52 + -2.475y + 1.52 + y2 = 0 + 1.52 Reorder the terms: -1.52 + 1.52 + -2.475y + y2 = 0 + 1.52 Combine like terms: -1.52 + 1.52 = 0.00 0.00 + -2.475y + y2 = 0 + 1.52 -2.475y + y2 = 0 + 1.52 Combine like terms: 0 + 1.52 = 1.52 -2.475y + y2 = 1.52 The y term is -2.475y. Take half its coefficient (-1.2375). Square it (1.53140625) and add it to both sides. Add '1.53140625' to each side of the equation. -2.475y + 1.53140625 + y2 = 1.52 + 1.53140625 Reorder the terms: 1.53140625 + -2.475y + y2 = 1.52 + 1.53140625 Combine like terms: 1.52 + 1.53140625 = 3.05140625 1.53140625 + -2.475y + y2 = 3.05140625 Factor a perfect square on the left side: (y + -1.2375)(y + -1.2375) = 3.05140625 Calculate the square root of the right side: 1.746827481 Break this problem into two subproblems by setting (y + -1.2375) equal to 1.746827481 and -1.746827481.Subproblem 1
y + -1.2375 = 1.746827481 Simplifying y + -1.2375 = 1.746827481 Reorder the terms: -1.2375 + y = 1.746827481 Solving -1.2375 + y = 1.746827481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2375' to each side of the equation. -1.2375 + 1.2375 + y = 1.746827481 + 1.2375 Combine like terms: -1.2375 + 1.2375 = 0.0000 0.0000 + y = 1.746827481 + 1.2375 y = 1.746827481 + 1.2375 Combine like terms: 1.746827481 + 1.2375 = 2.984327481 y = 2.984327481 Simplifying y = 2.984327481Subproblem 2
y + -1.2375 = -1.746827481 Simplifying y + -1.2375 = -1.746827481 Reorder the terms: -1.2375 + y = -1.746827481 Solving -1.2375 + y = -1.746827481 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.2375' to each side of the equation. -1.2375 + 1.2375 + y = -1.746827481 + 1.2375 Combine like terms: -1.2375 + 1.2375 = 0.0000 0.0000 + y = -1.746827481 + 1.2375 y = -1.746827481 + 1.2375 Combine like terms: -1.746827481 + 1.2375 = -0.509327481 y = -0.509327481 Simplifying y = -0.509327481Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.984327481, -0.509327481}
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