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Simplifying y3 + -14y2 + -48y = 0 Reorder the terms: -48y + -14y2 + y3 = 0 Solving -48y + -14y2 + y3 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), 'y'. y(-48 + -14y + y2) = 0Subproblem 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 '(-48 + -14y + y2)' equal to zero and attempt to solve: Simplifying -48 + -14y + y2 = 0 Solving -48 + -14y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '48' to each side of the equation. -48 + -14y + 48 + y2 = 0 + 48 Reorder the terms: -48 + 48 + -14y + y2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -14y + y2 = 0 + 48 -14y + y2 = 0 + 48 Combine like terms: 0 + 48 = 48 -14y + y2 = 48 The y term is -14y. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14y + 49 + y2 = 48 + 49 Reorder the terms: 49 + -14y + y2 = 48 + 49 Combine like terms: 48 + 49 = 97 49 + -14y + y2 = 97 Factor a perfect square on the left side: (y + -7)(y + -7) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (y + -7) equal to 9.848857802 and -9.848857802.Subproblem 1
y + -7 = 9.848857802 Simplifying y + -7 = 9.848857802 Reorder the terms: -7 + y = 9.848857802 Solving -7 + y = 9.848857802 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = 9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + y = 9.848857802 + 7 y = 9.848857802 + 7 Combine like terms: 9.848857802 + 7 = 16.848857802 y = 16.848857802 Simplifying y = 16.848857802Subproblem 2
y + -7 = -9.848857802 Simplifying y + -7 = -9.848857802 Reorder the terms: -7 + y = -9.848857802 Solving -7 + y = -9.848857802 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + y = -9.848857802 + 7 Combine like terms: -7 + 7 = 0 0 + y = -9.848857802 + 7 y = -9.848857802 + 7 Combine like terms: -9.848857802 + 7 = -2.848857802 y = -2.848857802 Simplifying y = -2.848857802Solution
The solution to the problem is based on the solutions from the subproblems. y = {16.848857802, -2.848857802}Solution
y = {0, 16.848857802, -2.848857802}
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