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Simplifying 3(y + -3) * 2y + -9 + y = 0 Reorder the terms: 3(-3 + y) * 2y + -9 + y = 0 Reorder the terms for easier multiplication: 3 * 2y(-3 + y) + -9 + y = 0 Multiply 3 * 2 6y(-3 + y) + -9 + y = 0 (-3 * 6y + y * 6y) + -9 + y = 0 (-18y + 6y2) + -9 + y = 0 Reorder the terms: -9 + -18y + y + 6y2 = 0 Combine like terms: -18y + y = -17y -9 + -17y + 6y2 = 0 Solving -9 + -17y + 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'. -1.5 + -2.833333333y + y2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.833333333y + 1.5 + y2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.833333333y + y2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.833333333y + y2 = 0 + 1.5 -2.833333333y + y2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.833333333y + y2 = 1.5 The y term is -2.833333333y. Take half its coefficient (-1.416666667). Square it (2.006944445) and add it to both sides. Add '2.006944445' to each side of the equation. -2.833333333y + 2.006944445 + y2 = 1.5 + 2.006944445 Reorder the terms: 2.006944445 + -2.833333333y + y2 = 1.5 + 2.006944445 Combine like terms: 1.5 + 2.006944445 = 3.506944445 2.006944445 + -2.833333333y + y2 = 3.506944445 Factor a perfect square on the left side: (y + -1.416666667)(y + -1.416666667) = 3.506944445 Calculate the square root of the right side: 1.872683755 Break this problem into two subproblems by setting (y + -1.416666667) equal to 1.872683755 and -1.872683755.Subproblem 1
y + -1.416666667 = 1.872683755 Simplifying y + -1.416666667 = 1.872683755 Reorder the terms: -1.416666667 + y = 1.872683755 Solving -1.416666667 + y = 1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + y = 1.872683755 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + y = 1.872683755 + 1.416666667 y = 1.872683755 + 1.416666667 Combine like terms: 1.872683755 + 1.416666667 = 3.289350422 y = 3.289350422 Simplifying y = 3.289350422Subproblem 2
y + -1.416666667 = -1.872683755 Simplifying y + -1.416666667 = -1.872683755 Reorder the terms: -1.416666667 + y = -1.872683755 Solving -1.416666667 + y = -1.872683755 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.416666667' to each side of the equation. -1.416666667 + 1.416666667 + y = -1.872683755 + 1.416666667 Combine like terms: -1.416666667 + 1.416666667 = 0.000000000 0.000000000 + y = -1.872683755 + 1.416666667 y = -1.872683755 + 1.416666667 Combine like terms: -1.872683755 + 1.416666667 = -0.456017088 y = -0.456017088 Simplifying y = -0.456017088Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.289350422, -0.456017088}
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