7a^2+2a-1=0

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Solution for 7a^2+2a-1=0 equation:


Simplifying
7a2 + 2a + -1 = 0

Reorder the terms:
-1 + 2a + 7a2 = 0

Solving
-1 + 2a + 7a2 = 0

Solving for variable 'a'.

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

Divide each side by '7'.
-0.1428571429 + 0.2857142857a + a2 = 0

Move the constant term to the right:

Add '0.1428571429' to each side of the equation.
-0.1428571429 + 0.2857142857a + 0.1428571429 + a2 = 0 + 0.1428571429

Reorder the terms:
-0.1428571429 + 0.1428571429 + 0.2857142857a + a2 = 0 + 0.1428571429

Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000
0.0000000000 + 0.2857142857a + a2 = 0 + 0.1428571429
0.2857142857a + a2 = 0 + 0.1428571429

Combine like terms: 0 + 0.1428571429 = 0.1428571429
0.2857142857a + a2 = 0.1428571429

The a term is 0.2857142857a.  Take half its coefficient (0.1428571429).
Square it (0.02040816328) and add it to both sides.

Add '0.02040816328' to each side of the equation.
0.2857142857a + 0.02040816328 + a2 = 0.1428571429 + 0.02040816328

Reorder the terms:
0.02040816328 + 0.2857142857a + a2 = 0.1428571429 + 0.02040816328

Combine like terms: 0.1428571429 + 0.02040816328 = 0.16326530618
0.02040816328 + 0.2857142857a + a2 = 0.16326530618

Factor a perfect square on the left side:
(a + 0.1428571429)(a + 0.1428571429) = 0.16326530618

Calculate the square root of the right side: 0.404061018

Break this problem into two subproblems by setting 
(a + 0.1428571429) equal to 0.404061018 and -0.404061018.

Subproblem 1

a + 0.1428571429 = 0.404061018 Simplifying a + 0.1428571429 = 0.404061018 Reorder the terms: 0.1428571429 + a = 0.404061018 Solving 0.1428571429 + a = 0.404061018 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + a = 0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + a = 0.404061018 + -0.1428571429 a = 0.404061018 + -0.1428571429 Combine like terms: 0.404061018 + -0.1428571429 = 0.2612038751 a = 0.2612038751 Simplifying a = 0.2612038751

Subproblem 2

a + 0.1428571429 = -0.404061018 Simplifying a + 0.1428571429 = -0.404061018 Reorder the terms: 0.1428571429 + a = -0.404061018 Solving 0.1428571429 + a = -0.404061018 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.1428571429' to each side of the equation. 0.1428571429 + -0.1428571429 + a = -0.404061018 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + a = -0.404061018 + -0.1428571429 a = -0.404061018 + -0.1428571429 Combine like terms: -0.404061018 + -0.1428571429 = -0.5469181609 a = -0.5469181609 Simplifying a = -0.5469181609

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.2612038751, -0.5469181609}

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