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Simplifying 7y2(3y2 + -9y + 2) = 0 Reorder the terms: 7y2(2 + -9y + 3y2) = 0 (2 * 7y2 + -9y * 7y2 + 3y2 * 7y2) = 0 (14y2 + -63y3 + 21y4) = 0 Solving 14y2 + -63y3 + 21y4 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7y2'. 7y2(2 + -9y + 3y2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'y2' equal to zero and attempt to solve: Simplifying y2 = 0 Solving y2 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y2 = 0 Take the square root of each side: y = {0}Subproblem 2
Set the factor '(2 + -9y + 3y2)' equal to zero and attempt to solve: Simplifying 2 + -9y + 3y2 = 0 Solving 2 + -9y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -3y + y2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -3y + -0.6666666667 + y2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -3y + y2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -3y + y2 = 0 + -0.6666666667 -3y + y2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -3y + y2 = -0.6666666667 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 = -0.6666666667 + 2.25 Reorder the terms: 2.25 + -3y + y2 = -0.6666666667 + 2.25 Combine like terms: -0.6666666667 + 2.25 = 1.5833333333 2.25 + -3y + y2 = 1.5833333333 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 1.5833333333 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (y + -1.5) equal to 1.258305739 and -1.258305739.Subproblem 1
y + -1.5 = 1.258305739 Simplifying y + -1.5 = 1.258305739 Reorder the terms: -1.5 + y = 1.258305739 Solving -1.5 + y = 1.258305739 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 = 1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 1.258305739 + 1.5 y = 1.258305739 + 1.5 Combine like terms: 1.258305739 + 1.5 = 2.758305739 y = 2.758305739 Simplifying y = 2.758305739Subproblem 2
y + -1.5 = -1.258305739 Simplifying y + -1.5 = -1.258305739 Reorder the terms: -1.5 + y = -1.258305739 Solving -1.5 + y = -1.258305739 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 = -1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -1.258305739 + 1.5 y = -1.258305739 + 1.5 Combine like terms: -1.258305739 + 1.5 = 0.241694261 y = 0.241694261 Simplifying y = 0.241694261Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.758305739, 0.241694261}Solution
y = {0, 2.758305739, 0.241694261}
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