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Simplifying 4y2 + -16y + 1 = 0 Reorder the terms: 1 + -16y + 4y2 = 0 Solving 1 + -16y + 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'. 0.25 + -4y + y2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + -4y + -0.25 + y2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + -4y + y2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + -4y + y2 = 0 + -0.25 -4y + y2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 -4y + y2 = -0.25 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -0.25 + 4 Reorder the terms: 4 + -4y + y2 = -0.25 + 4 Combine like terms: -0.25 + 4 = 3.75 4 + -4y + y2 = 3.75 Factor a perfect square on the left side: (y + -2)(y + -2) = 3.75 Calculate the square root of the right side: 1.936491673 Break this problem into two subproblems by setting (y + -2) equal to 1.936491673 and -1.936491673.Subproblem 1
y + -2 = 1.936491673 Simplifying y + -2 = 1.936491673 Reorder the terms: -2 + y = 1.936491673 Solving -2 + y = 1.936491673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + y = 1.936491673 + 2 y = 1.936491673 + 2 Combine like terms: 1.936491673 + 2 = 3.936491673 y = 3.936491673 Simplifying y = 3.936491673Subproblem 2
y + -2 = -1.936491673 Simplifying y + -2 = -1.936491673 Reorder the terms: -2 + y = -1.936491673 Solving -2 + y = -1.936491673 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -1.936491673 + 2 Combine like terms: -2 + 2 = 0 0 + y = -1.936491673 + 2 y = -1.936491673 + 2 Combine like terms: -1.936491673 + 2 = 0.063508327 y = 0.063508327 Simplifying y = 0.063508327Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.936491673, 0.063508327}
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