4x^2+6x-49=0

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Solution for 4x^2+6x-49=0 equation: 


Simplifying
4x2 + 6x + -49 = 0

Reorder the terms:
-49 + 6x + 4x2 = 0

Solving
-49 + 6x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-12.25 + 1.5x + x2 = 0

Move the constant term to the right:

Add '12.25' to each side of the equation.
-12.25 + 1.5x + 12.25 + x2 = 0 + 12.25

Reorder the terms:
-12.25 + 12.25 + 1.5x + x2 = 0 + 12.25

Combine like terms: -12.25 + 12.25 = 0.00
0.00 + 1.5x + x2 = 0 + 12.25
1.5x + x2 = 0 + 12.25

Combine like terms: 0 + 12.25 = 12.25
1.5x + x2 = 12.25

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 12.25 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 12.25 + 0.5625

Combine like terms: 12.25 + 0.5625 = 12.8125
0.5625 + 1.5x + x2 = 12.8125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 12.8125

Calculate the square root of the right side: 3.579455266

Break this problem into two subproblems by setting 
(x + 0.75) equal to 3.579455266 and -3.579455266.


Subproblem 1
x + 0.75 = 3.579455266

Simplifying
x + 0.75 = 3.579455266

Reorder the terms:
0.75 + x = 3.579455266

Solving
0.75 + x = 3.579455266

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 3.579455266 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 3.579455266 + -0.75
x = 3.579455266 + -0.75

Combine like terms: 3.579455266 + -0.75 = 2.829455266
x = 2.829455266

Simplifying
x = 2.829455266


Subproblem 2
x + 0.75 = -3.579455266

Simplifying
x + 0.75 = -3.579455266

Reorder the terms:
0.75 + x = -3.579455266

Solving
0.75 + x = -3.579455266

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -3.579455266 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -3.579455266 + -0.75
x = -3.579455266 + -0.75

Combine like terms: -3.579455266 + -0.75 = -4.329455266
x = -4.329455266

Simplifying
x = -4.329455266


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.829455266, -4.329455266}

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