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Simplifying 5y(7y2 + -4y + -2) = 0 Reorder the terms: 5y(-2 + -4y + 7y2) = 0 (-2 * 5y + -4y * 5y + 7y2 * 5y) = 0 (-10y + -20y2 + 35y3) = 0 Solving -10y + -20y2 + 35y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(-2 + -4y + 7y2) = 0 Ignore the factor 5.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 '(-2 + -4y + 7y2)' equal to zero and attempt to solve: Simplifying -2 + -4y + 7y2 = 0 Solving -2 + -4y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -0.2857142857 + -0.5714285714y + y2 = 0 Move the constant term to the right: Add '0.2857142857' to each side of the equation. -0.2857142857 + -0.5714285714y + 0.2857142857 + y2 = 0 + 0.2857142857 Reorder the terms: -0.2857142857 + 0.2857142857 + -0.5714285714y + y2 = 0 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + -0.5714285714y + y2 = 0 + 0.2857142857 -0.5714285714y + y2 = 0 + 0.2857142857 Combine like terms: 0 + 0.2857142857 = 0.2857142857 -0.5714285714y + y2 = 0.2857142857 The y term is -0.5714285714y. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714y + 0.08163265305 + y2 = 0.2857142857 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714y + y2 = 0.2857142857 + 0.08163265305 Combine like terms: 0.2857142857 + 0.08163265305 = 0.36734693875 0.08163265305 + -0.5714285714y + y2 = 0.36734693875 Factor a perfect square on the left side: (y + -0.2857142857)(y + -0.2857142857) = 0.36734693875 Calculate the square root of the right side: 0.606091527 Break this problem into two subproblems by setting (y + -0.2857142857) equal to 0.606091527 and -0.606091527.Subproblem 1
y + -0.2857142857 = 0.606091527 Simplifying y + -0.2857142857 = 0.606091527 Reorder the terms: -0.2857142857 + y = 0.606091527 Solving -0.2857142857 + y = 0.606091527 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + y = 0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + y = 0.606091527 + 0.2857142857 y = 0.606091527 + 0.2857142857 Combine like terms: 0.606091527 + 0.2857142857 = 0.8918058127 y = 0.8918058127 Simplifying y = 0.8918058127Subproblem 2
y + -0.2857142857 = -0.606091527 Simplifying y + -0.2857142857 = -0.606091527 Reorder the terms: -0.2857142857 + y = -0.606091527 Solving -0.2857142857 + y = -0.606091527 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + y = -0.606091527 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + y = -0.606091527 + 0.2857142857 y = -0.606091527 + 0.2857142857 Combine like terms: -0.606091527 + 0.2857142857 = -0.3203772413 y = -0.3203772413 Simplifying y = -0.3203772413Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.8918058127, -0.3203772413}Solution
y = {0, 0.8918058127, -0.3203772413}
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