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Simplifying 35y3 + -7y + 14y2 = 0 Reorder the terms: -7y + 14y2 + 35y3 = 0 Solving -7y + 14y2 + 35y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '7y'. 7y(-1 + 2y + 5y2) = 0 Ignore the factor 7.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 '(-1 + 2y + 5y2)' equal to zero and attempt to solve: Simplifying -1 + 2y + 5y2 = 0 Solving -1 + 2y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + 0.4y + y2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 0.4y + 0.2 + y2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 0.4y + y2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 0.4y + y2 = 0 + 0.2 0.4y + y2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 0.4y + y2 = 0.2 The y term is 0.4y. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4y + 0.04 + y2 = 0.2 + 0.04 Reorder the terms: 0.04 + 0.4y + y2 = 0.2 + 0.04 Combine like terms: 0.2 + 0.04 = 0.24 0.04 + 0.4y + y2 = 0.24 Factor a perfect square on the left side: (y + 0.2)(y + 0.2) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (y + 0.2) equal to 0.489897949 and -0.489897949.Subproblem 1
y + 0.2 = 0.489897949 Simplifying y + 0.2 = 0.489897949 Reorder the terms: 0.2 + y = 0.489897949 Solving 0.2 + y = 0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = 0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = 0.489897949 + -0.2 y = 0.489897949 + -0.2 Combine like terms: 0.489897949 + -0.2 = 0.289897949 y = 0.289897949 Simplifying y = 0.289897949Subproblem 2
y + 0.2 = -0.489897949 Simplifying y + 0.2 = -0.489897949 Reorder the terms: 0.2 + y = -0.489897949 Solving 0.2 + y = -0.489897949 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + y = -0.489897949 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + y = -0.489897949 + -0.2 y = -0.489897949 + -0.2 Combine like terms: -0.489897949 + -0.2 = -0.689897949 y = -0.689897949 Simplifying y = -0.689897949Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.289897949, -0.689897949}Solution
y = {0, 0.289897949, -0.689897949}
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