a^3-2a^2-3a^2-4a=

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Solution for a^3-2a^2-3a^2-4a= equation:


Simplifying
a3 + -2a2 + -3a2 + -4a = 0

Reorder the terms:
-4a + -2a2 + -3a2 + a3 = 0

Combine like terms: -2a2 + -3a2 = -5a2
-4a + -5a2 + a3 = 0

Solving
-4a + -5a2 + a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-4 + -5a + a2) = 0

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(-4 + -5a + a2)' equal to zero and attempt to solve: Simplifying -4 + -5a + a2 = 0 Solving -4 + -5a + a2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5a + 4 + a2 = 0 + 4 Reorder the terms: -4 + 4 + -5a + a2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5a + a2 = 0 + 4 -5a + a2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5a + a2 = 4 The a term is -5a. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5a + 6.25 + a2 = 4 + 6.25 Reorder the terms: 6.25 + -5a + a2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5a + a2 = 10.25 Factor a perfect square on the left side: (a + -2.5)(a + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (a + -2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

a + -2.5 = 3.201562119 Simplifying a + -2.5 = 3.201562119 Reorder the terms: -2.5 + a = 3.201562119 Solving -2.5 + a = 3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = 3.201562119 + 2.5 a = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 a = 5.701562119 Simplifying a = 5.701562119

Subproblem 2

a + -2.5 = -3.201562119 Simplifying a + -2.5 = -3.201562119 Reorder the terms: -2.5 + a = -3.201562119 Solving -2.5 + a = -3.201562119 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + a = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + a = -3.201562119 + 2.5 a = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 a = -0.701562119 Simplifying a = -0.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.701562119, -0.701562119}

Solution

a = {0, 5.701562119, -0.701562119}

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