8x^2+40x+49=0

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Solution for 8x^2+40x+49=0 equation: 


Simplifying
8x2 + 40x + 49 = 0

Reorder the terms:
49 + 40x + 8x2 = 0

Solving
49 + 40x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
6.125 + 5x + x2 = 0

Move the constant term to the right:

Add '-6.125' to each side of the equation.
6.125 + 5x + -6.125 + x2 = 0 + -6.125

Reorder the terms:
6.125 + -6.125 + 5x + x2 = 0 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + 5x + x2 = 0 + -6.125
5x + x2 = 0 + -6.125

Combine like terms: 0 + -6.125 = -6.125
5x + x2 = -6.125

The x term is 5x.  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.
5x + 6.25 + x2 = -6.125 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -6.125 + 6.25

Combine like terms: -6.125 + 6.25 = 0.125
6.25 + 5x + x2 = 0.125

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(x + 2.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
x + 2.5 = 0.353553391

Simplifying
x + 2.5 = 0.353553391

Reorder the terms:
2.5 + x = 0.353553391

Solving
2.5 + x = 0.353553391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 0.353553391 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 0.353553391 + -2.5
x = 0.353553391 + -2.5

Combine like terms: 0.353553391 + -2.5 = -2.146446609
x = -2.146446609

Simplifying
x = -2.146446609


Subproblem 2
x + 2.5 = -0.353553391

Simplifying
x + 2.5 = -0.353553391

Reorder the terms:
2.5 + x = -0.353553391

Solving
2.5 + x = -0.353553391

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -0.353553391 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -0.353553391 + -2.5
x = -0.353553391 + -2.5

Combine like terms: -0.353553391 + -2.5 = -2.853553391
x = -2.853553391

Simplifying
x = -2.853553391


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.146446609, -2.853553391}

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