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Simplifying (4y2 + -13y + 2) = 0 Reorder the terms: (2 + -13y + 4y2) = 0 Remove parenthesis around (2 + -13y + 4y2) 2 + -13y + 4y2 = 0 Solving 2 + -13y + 4y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.5 + -3.25y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -3.25y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -3.25y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -3.25y + y2 = 0 + -0.5 -3.25y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -3.25y + y2 = -0.5 The y term is -3.25y. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25y + 2.640625 + y2 = -0.5 + 2.640625 Reorder the terms: 2.640625 + -3.25y + y2 = -0.5 + 2.640625 Combine like terms: -0.5 + 2.640625 = 2.140625 2.640625 + -3.25y + y2 = 2.140625 Factor a perfect square on the left side: (y + -1.625)(y + -1.625) = 2.140625 Calculate the square root of the right side: 1.463087489 Break this problem into two subproblems by setting (y + -1.625) equal to 1.463087489 and -1.463087489.Subproblem 1
y + -1.625 = 1.463087489 Simplifying y + -1.625 = 1.463087489 Reorder the terms: -1.625 + y = 1.463087489 Solving -1.625 + y = 1.463087489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = 1.463087489 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = 1.463087489 + 1.625 y = 1.463087489 + 1.625 Combine like terms: 1.463087489 + 1.625 = 3.088087489 y = 3.088087489 Simplifying y = 3.088087489Subproblem 2
y + -1.625 = -1.463087489 Simplifying y + -1.625 = -1.463087489 Reorder the terms: -1.625 + y = -1.463087489 Solving -1.625 + y = -1.463087489 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + y = -1.463087489 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + y = -1.463087489 + 1.625 y = -1.463087489 + 1.625 Combine like terms: -1.463087489 + 1.625 = 0.161912511 y = 0.161912511 Simplifying y = 0.161912511Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.088087489, 0.161912511}
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