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Simplifying 0 = 4y2 + -12y + -5 Reorder the terms: 0 = -5 + -12y + 4y2 Solving 0 = -5 + -12y + 4y2 Solving for variable 'y'. Combine like terms: 0 + 5 = 5 5 + 12y + -4y2 = -5 + -12y + 4y2 + 5 + 12y + -4y2 Reorder the terms: 5 + 12y + -4y2 = -5 + 5 + -12y + 12y + 4y2 + -4y2 Combine like terms: -5 + 5 = 0 5 + 12y + -4y2 = 0 + -12y + 12y + 4y2 + -4y2 5 + 12y + -4y2 = -12y + 12y + 4y2 + -4y2 Combine like terms: -12y + 12y = 0 5 + 12y + -4y2 = 0 + 4y2 + -4y2 5 + 12y + -4y2 = 4y2 + -4y2 Combine like terms: 4y2 + -4y2 = 0 5 + 12y + -4y2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1.25 + -3y + y2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -3y + 1.25 + y2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -3y + y2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -3y + y2 = 0 + 1.25 -3y + y2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -3y + y2 = 1.25 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 1.25 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 1.25 + 2.25 Combine like terms: 1.25 + 2.25 = 3.5 2.25 + -3y + y2 = 3.5 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 3.5 Calculate the square root of the right side: 1.870828693 Break this problem into two subproblems by setting (y + -1.5) equal to 1.870828693 and -1.870828693.Subproblem 1
y + -1.5 = 1.870828693 Simplifying y + -1.5 = 1.870828693 Reorder the terms: -1.5 + y = 1.870828693 Solving -1.5 + y = 1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.870828693 + 1.5 y = 1.870828693 + 1.5 Combine like terms: 1.870828693 + 1.5 = 3.370828693 y = 3.370828693 Simplifying y = 3.370828693Subproblem 2
y + -1.5 = -1.870828693 Simplifying y + -1.5 = -1.870828693 Reorder the terms: -1.5 + y = -1.870828693 Solving -1.5 + y = -1.870828693 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -1.870828693 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.870828693 + 1.5 y = -1.870828693 + 1.5 Combine like terms: -1.870828693 + 1.5 = -0.370828693 y = -0.370828693 Simplifying y = -0.370828693Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.370828693, -0.370828693}
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