2a+5a(a-1)=6

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Solution for 2a+5a(a-1)=6 equation:


Simplifying
2a + 5a(a + -1) = 6

Reorder the terms:
2a + 5a(-1 + a) = 6
2a + (-1 * 5a + a * 5a) = 6
2a + (-5a + 5a2) = 6

Combine like terms: 2a + -5a = -3a
-3a + 5a2 = 6

Solving
-3a + 5a2 = 6

Solving for variable 'a'.

Reorder the terms:
-6 + -3a + 5a2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -3a + 5a2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.2 + -0.6a + a2 = 0

Move the constant term to the right:

Add '1.2' to each side of the equation.
-1.2 + -0.6a + 1.2 + a2 = 0 + 1.2

Reorder the terms:
-1.2 + 1.2 + -0.6a + a2 = 0 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + -0.6a + a2 = 0 + 1.2
-0.6a + a2 = 0 + 1.2

Combine like terms: 0 + 1.2 = 1.2
-0.6a + a2 = 1.2

The a term is -0.6a.  Take half its coefficient (-0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
-0.6a + 0.09 + a2 = 1.2 + 0.09

Reorder the terms:
0.09 + -0.6a + a2 = 1.2 + 0.09

Combine like terms: 1.2 + 0.09 = 1.29
0.09 + -0.6a + a2 = 1.29

Factor a perfect square on the left side:
(a + -0.3)(a + -0.3) = 1.29

Calculate the square root of the right side: 1.135781669

Break this problem into two subproblems by setting 
(a + -0.3) equal to 1.135781669 and -1.135781669.

Subproblem 1

a + -0.3 = 1.135781669 Simplifying a + -0.3 = 1.135781669 Reorder the terms: -0.3 + a = 1.135781669 Solving -0.3 + a = 1.135781669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + a = 1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + a = 1.135781669 + 0.3 a = 1.135781669 + 0.3 Combine like terms: 1.135781669 + 0.3 = 1.435781669 a = 1.435781669 Simplifying a = 1.435781669

Subproblem 2

a + -0.3 = -1.135781669 Simplifying a + -0.3 = -1.135781669 Reorder the terms: -0.3 + a = -1.135781669 Solving -0.3 + a = -1.135781669 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + a = -1.135781669 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + a = -1.135781669 + 0.3 a = -1.135781669 + 0.3 Combine like terms: -1.135781669 + 0.3 = -0.835781669 a = -0.835781669 Simplifying a = -0.835781669

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.435781669, -0.835781669}

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