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Simplifying 3y(2y2 + -4y + -7) = 0 Reorder the terms: 3y(-7 + -4y + 2y2) = 0 (-7 * 3y + -4y * 3y + 2y2 * 3y) = 0 (-21y + -12y2 + 6y3) = 0 Solving -21y + -12y2 + 6y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3y'. 3y(-7 + -4y + 2y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor 'y' equal to zero and attempt to solve: Simplifying y = 0 Solving y = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y = 0Subproblem 2
Set the factor '(-7 + -4y + 2y2)' equal to zero and attempt to solve: Simplifying -7 + -4y + 2y2 = 0 Solving -7 + -4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + -2y + y2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + -2y + 3.5 + y2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + -2y + y2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + -2y + y2 = 0 + 3.5 -2y + y2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 -2y + y2 = 3.5 The y term is -2y. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2y + 1 + y2 = 3.5 + 1 Reorder the terms: 1 + -2y + y2 = 3.5 + 1 Combine like terms: 3.5 + 1 = 4.5 1 + -2y + y2 = 4.5 Factor a perfect square on the left side: (y + -1)(y + -1) = 4.5 Calculate the square root of the right side: 2.121320344 Break this problem into two subproblems by setting (y + -1) equal to 2.121320344 and -2.121320344.Subproblem 1
y + -1 = 2.121320344 Simplifying y + -1 = 2.121320344 Reorder the terms: -1 + y = 2.121320344 Solving -1 + y = 2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = 2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + y = 2.121320344 + 1 y = 2.121320344 + 1 Combine like terms: 2.121320344 + 1 = 3.121320344 y = 3.121320344 Simplifying y = 3.121320344Subproblem 2
y + -1 = -2.121320344 Simplifying y + -1 = -2.121320344 Reorder the terms: -1 + y = -2.121320344 Solving -1 + y = -2.121320344 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + y = -2.121320344 + 1 Combine like terms: -1 + 1 = 0 0 + y = -2.121320344 + 1 y = -2.121320344 + 1 Combine like terms: -2.121320344 + 1 = -1.121320344 y = -1.121320344 Simplifying y = -1.121320344Solution
The solution to the problem is based on the solutions from the subproblems. y = {3.121320344, -1.121320344}Solution
y = {0, 3.121320344, -1.121320344}
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