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Simplifying 4y2 + 22y + 25 = 0 Reorder the terms: 25 + 22y + 4y2 = 0 Solving 25 + 22y + 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'. 6.25 + 5.5y + y2 = 0 Move the constant term to the right: Add '-6.25' to each side of the equation. 6.25 + 5.5y + -6.25 + y2 = 0 + -6.25 Reorder the terms: 6.25 + -6.25 + 5.5y + y2 = 0 + -6.25 Combine like terms: 6.25 + -6.25 = 0.00 0.00 + 5.5y + y2 = 0 + -6.25 5.5y + y2 = 0 + -6.25 Combine like terms: 0 + -6.25 = -6.25 5.5y + y2 = -6.25 The y term is 5.5y. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5y + 7.5625 + y2 = -6.25 + 7.5625 Reorder the terms: 7.5625 + 5.5y + y2 = -6.25 + 7.5625 Combine like terms: -6.25 + 7.5625 = 1.3125 7.5625 + 5.5y + y2 = 1.3125 Factor a perfect square on the left side: (y + 2.75)(y + 2.75) = 1.3125 Calculate the square root of the right side: 1.145643924 Break this problem into two subproblems by setting (y + 2.75) equal to 1.145643924 and -1.145643924.Subproblem 1
y + 2.75 = 1.145643924 Simplifying y + 2.75 = 1.145643924 Reorder the terms: 2.75 + y = 1.145643924 Solving 2.75 + y = 1.145643924 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = 1.145643924 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = 1.145643924 + -2.75 y = 1.145643924 + -2.75 Combine like terms: 1.145643924 + -2.75 = -1.604356076 y = -1.604356076 Simplifying y = -1.604356076Subproblem 2
y + 2.75 = -1.145643924 Simplifying y + 2.75 = -1.145643924 Reorder the terms: 2.75 + y = -1.145643924 Solving 2.75 + y = -1.145643924 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + y = -1.145643924 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + y = -1.145643924 + -2.75 y = -1.145643924 + -2.75 Combine like terms: -1.145643924 + -2.75 = -3.895643924 y = -3.895643924 Simplifying y = -3.895643924Solution
The solution to the problem is based on the solutions from the subproblems. y = {-1.604356076, -3.895643924}
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