1-5a^2+2a+4a=

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Solution for 1-5a^2+2a+4a= equation:


Simplifying
1 + -5a2 + 2a + 4a = 0

Reorder the terms:
1 + 2a + 4a + -5a2 = 0

Combine like terms: 2a + 4a = 6a
1 + 6a + -5a2 = 0

Solving
1 + 6a + -5a2 = 0

Solving for variable 'a'.

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

Divide each side by '-5'.
-0.2 + -1.2a + a2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -1.2a + 0.2 + a2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -1.2a + a2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -1.2a + a2 = 0 + 0.2
-1.2a + a2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-1.2a + a2 = 0.2

The a term is -1.2a.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2a + 0.36 + a2 = 0.2 + 0.36

Reorder the terms:
0.36 + -1.2a + a2 = 0.2 + 0.36

Combine like terms: 0.2 + 0.36 = 0.56
0.36 + -1.2a + a2 = 0.56

Factor a perfect square on the left side:
(a + -0.6)(a + -0.6) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(a + -0.6) equal to 0.748331477 and -0.748331477.

Subproblem 1

a + -0.6 = 0.748331477 Simplifying a + -0.6 = 0.748331477 Reorder the terms: -0.6 + a = 0.748331477 Solving -0.6 + a = 0.748331477 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + a = 0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + a = 0.748331477 + 0.6 a = 0.748331477 + 0.6 Combine like terms: 0.748331477 + 0.6 = 1.348331477 a = 1.348331477 Simplifying a = 1.348331477

Subproblem 2

a + -0.6 = -0.748331477 Simplifying a + -0.6 = -0.748331477 Reorder the terms: -0.6 + a = -0.748331477 Solving -0.6 + a = -0.748331477 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + a = -0.748331477 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + a = -0.748331477 + 0.6 a = -0.748331477 + 0.6 Combine like terms: -0.748331477 + 0.6 = -0.148331477 a = -0.148331477 Simplifying a = -0.148331477

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.348331477, -0.148331477}

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