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Simplifying 7y4(2y2 + -7y + 4) = 0 Reorder the terms: 7y4(4 + -7y + 2y2) = 0 (4 * 7y4 + -7y * 7y4 + 2y2 * 7y4) = 0 (28y4 + -49y5 + 14y6) = 0 Solving 28y4 + -49y5 + 14y6 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7y4'. 7y4(4 + -7y + 2y2) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'y4' equal to zero and attempt to solve: Simplifying y4 = 0 Solving y4 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(4 + -7y + 2y2)' equal to zero and attempt to solve: Simplifying 4 + -7y + 2y2 = 0 Solving 4 + -7y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + -3.5y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.5y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -3.5y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.5y + y2 = 0 + -2 -3.5y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.5y + y2 = -2 The y term is -3.5y. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5y + 3.0625 + y2 = -2 + 3.0625 Reorder the terms: 3.0625 + -3.5y + y2 = -2 + 3.0625 Combine like terms: -2 + 3.0625 = 1.0625 3.0625 + -3.5y + y2 = 1.0625 Factor a perfect square on the left side: (y + -1.75)(y + -1.75) = 1.0625 Calculate the square root of the right side: 1.030776406 Break this problem into two subproblems by setting (y + -1.75) equal to 1.030776406 and -1.030776406.Subproblem 1
y + -1.75 = 1.030776406 Simplifying y + -1.75 = 1.030776406 Reorder the terms: -1.75 + y = 1.030776406 Solving -1.75 + y = 1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = 1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = 1.030776406 + 1.75 y = 1.030776406 + 1.75 Combine like terms: 1.030776406 + 1.75 = 2.780776406 y = 2.780776406 Simplifying y = 2.780776406Subproblem 2
y + -1.75 = -1.030776406 Simplifying y + -1.75 = -1.030776406 Reorder the terms: -1.75 + y = -1.030776406 Solving -1.75 + y = -1.030776406 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + y = -1.030776406 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + y = -1.030776406 + 1.75 y = -1.030776406 + 1.75 Combine like terms: -1.030776406 + 1.75 = 0.719223594 y = 0.719223594 Simplifying y = 0.719223594Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.780776406, 0.719223594}Solution
y = {2.780776406, 0.719223594}
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