49a^2+49a+49a+49+4a+4-2=0

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Solution for 49a^2+49a+49a+49+4a+4-2=0 equation:


Simplifying
49a2 + 49a + 49a + 49 + 4a + 4 + -2 = 0

Reorder the terms:
49 + 4 + -2 + 49a + 49a + 4a + 49a2 = 0

Combine like terms: 49 + 4 = 53
53 + -2 + 49a + 49a + 4a + 49a2 = 0

Combine like terms: 53 + -2 = 51
51 + 49a + 49a + 4a + 49a2 = 0

Combine like terms: 49a + 49a = 98a
51 + 98a + 4a + 49a2 = 0

Combine like terms: 98a + 4a = 102a
51 + 102a + 49a2 = 0

Solving
51 + 102a + 49a2 = 0

Solving for variable 'a'.

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

Divide each side by '49'.
1.040816327 + 2.081632653a + a2 = 0

Move the constant term to the right:

Add '-1.040816327' to each side of the equation.
1.040816327 + 2.081632653a + -1.040816327 + a2 = 0 + -1.040816327

Reorder the terms:
1.040816327 + -1.040816327 + 2.081632653a + a2 = 0 + -1.040816327

Combine like terms: 1.040816327 + -1.040816327 = 0.000000000
0.000000000 + 2.081632653a + a2 = 0 + -1.040816327
2.081632653a + a2 = 0 + -1.040816327

Combine like terms: 0 + -1.040816327 = -1.040816327
2.081632653a + a2 = -1.040816327

The a term is 2.081632653a.  Take half its coefficient (1.040816327).
Square it (1.083298627) and add it to both sides.

Add '1.083298627' to each side of the equation.
2.081632653a + 1.083298627 + a2 = -1.040816327 + 1.083298627

Reorder the terms:
1.083298627 + 2.081632653a + a2 = -1.040816327 + 1.083298627

Combine like terms: -1.040816327 + 1.083298627 = 0.0424823
1.083298627 + 2.081632653a + a2 = 0.0424823

Factor a perfect square on the left side:
(a + 1.040816327)(a + 1.040816327) = 0.0424823

Calculate the square root of the right side: 0.206112348

Break this problem into two subproblems by setting 
(a + 1.040816327) equal to 0.206112348 and -0.206112348.

Subproblem 1

a + 1.040816327 = 0.206112348 Simplifying a + 1.040816327 = 0.206112348 Reorder the terms: 1.040816327 + a = 0.206112348 Solving 1.040816327 + a = 0.206112348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.040816327' to each side of the equation. 1.040816327 + -1.040816327 + a = 0.206112348 + -1.040816327 Combine like terms: 1.040816327 + -1.040816327 = 0.000000000 0.000000000 + a = 0.206112348 + -1.040816327 a = 0.206112348 + -1.040816327 Combine like terms: 0.206112348 + -1.040816327 = -0.834703979 a = -0.834703979 Simplifying a = -0.834703979

Subproblem 2

a + 1.040816327 = -0.206112348 Simplifying a + 1.040816327 = -0.206112348 Reorder the terms: 1.040816327 + a = -0.206112348 Solving 1.040816327 + a = -0.206112348 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.040816327' to each side of the equation. 1.040816327 + -1.040816327 + a = -0.206112348 + -1.040816327 Combine like terms: 1.040816327 + -1.040816327 = 0.000000000 0.000000000 + a = -0.206112348 + -1.040816327 a = -0.206112348 + -1.040816327 Combine like terms: -0.206112348 + -1.040816327 = -1.246928675 a = -1.246928675 Simplifying a = -1.246928675

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.834703979, -1.246928675}

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