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Simplifying 6y2 + -15y + 4 = 0 Reorder the terms: 4 + -15y + 6y2 = 0 Solving 4 + -15y + 6y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 0.6666666667 + -2.5y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -2.5y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -2.5y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -2.5y + y2 = 0 + -0.6666666667 -2.5y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -2.5y + y2 = -0.6666666667 The y term is -2.5y. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5y + 1.5625 + y2 = -0.6666666667 + 1.5625 Reorder the terms: 1.5625 + -2.5y + y2 = -0.6666666667 + 1.5625 Combine like terms: -0.6666666667 + 1.5625 = 0.8958333333 1.5625 + -2.5y + y2 = 0.8958333333 Factor a perfect square on the left side: (y + -1.25)(y + -1.25) = 0.8958333333 Calculate the square root of the right side: 0.946484724 Break this problem into two subproblems by setting (y + -1.25) equal to 0.946484724 and -0.946484724.Subproblem 1
y + -1.25 = 0.946484724 Simplifying y + -1.25 = 0.946484724 Reorder the terms: -1.25 + y = 0.946484724 Solving -1.25 + y = 0.946484724 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = 0.946484724 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = 0.946484724 + 1.25 y = 0.946484724 + 1.25 Combine like terms: 0.946484724 + 1.25 = 2.196484724 y = 2.196484724 Simplifying y = 2.196484724Subproblem 2
y + -1.25 = -0.946484724 Simplifying y + -1.25 = -0.946484724 Reorder the terms: -1.25 + y = -0.946484724 Solving -1.25 + y = -0.946484724 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + y = -0.946484724 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + y = -0.946484724 + 1.25 y = -0.946484724 + 1.25 Combine like terms: -0.946484724 + 1.25 = 0.303515276 y = 0.303515276 Simplifying y = 0.303515276Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.196484724, 0.303515276}
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