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Simplifying 5y(-1y2 + 7y + -2) = 0 Reorder the terms: 5y(-2 + 7y + -1y2) = 0 (-2 * 5y + 7y * 5y + -1y2 * 5y) = 0 (-10y + 35y2 + -5y3) = 0 Solving -10y + 35y2 + -5y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y'. 5y(-2 + 7y + -1y2) = 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 + 7y + -1y2)' equal to zero and attempt to solve: Simplifying -2 + 7y + -1y2 = 0 Solving -2 + 7y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -7y + y2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -7y + -2 + y2 = 0 + -2 Reorder the terms: 2 + -2 + -7y + y2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7y + y2 = 0 + -2 -7y + y2 = 0 + -2 Combine like terms: 0 + -2 = -2 -7y + y2 = -2 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = -2 + 12.25 Reorder the terms: 12.25 + -7y + y2 = -2 + 12.25 Combine like terms: -2 + 12.25 = 10.25 12.25 + -7y + y2 = 10.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + -3.5) equal to 3.201562119 and -3.201562119.Subproblem 1
y + -3.5 = 3.201562119 Simplifying y + -3.5 = 3.201562119 Reorder the terms: -3.5 + y = 3.201562119 Solving -3.5 + y = 3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 3.201562119 + 3.5 y = 3.201562119 + 3.5 Combine like terms: 3.201562119 + 3.5 = 6.701562119 y = 6.701562119 Simplifying y = 6.701562119Subproblem 2
y + -3.5 = -3.201562119 Simplifying y + -3.5 = -3.201562119 Reorder the terms: -3.5 + y = -3.201562119 Solving -3.5 + y = -3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -3.201562119 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -3.201562119 + 3.5 y = -3.201562119 + 3.5 Combine like terms: -3.201562119 + 3.5 = 0.298437881 y = 0.298437881 Simplifying y = 0.298437881Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.701562119, 0.298437881}Solution
y = {0, 6.701562119, 0.298437881}
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