6x^2+28x+49=44

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Solution for 6x^2+28x+49=44 equation:


Simplifying
6x2 + 28x + 49 = 44

Reorder the terms:
49 + 28x + 6x2 = 44

Solving
49 + 28x + 6x2 = 44

Solving for variable 'x'.

Reorder the terms:
49 + -44 + 28x + 6x2 = 44 + -44

Combine like terms: 49 + -44 = 5
5 + 28x + 6x2 = 44 + -44

Combine like terms: 44 + -44 = 0
5 + 28x + 6x2 = 0

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

Divide each side by '6'.
0.8333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.8333333333' to each side of the equation.
0.8333333333 + 4.666666667x + -0.8333333333 + x2 = 0 + -0.8333333333

Reorder the terms:
0.8333333333 + -0.8333333333 + 4.666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000
0.0000000000 + 4.666666667x + x2 = 0 + -0.8333333333
4.666666667x + x2 = 0 + -0.8333333333

Combine like terms: 0 + -0.8333333333 = -0.8333333333
4.666666667x + x2 = -0.8333333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -0.8333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -0.8333333333 + 5.444444448

Combine like terms: -0.8333333333 + 5.444444448 = 4.6111111147
5.444444448 + 4.666666667x + x2 = 4.6111111147

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 4.6111111147

Calculate the square root of the right side: 2.147349789

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.147349789 and -2.147349789.


Subproblem 1
x + 2.333333334 = 2.147349789

Simplifying
x + 2.333333334 = 2.147349789

Reorder the terms:
2.333333334 + x = 2.147349789

Solving
2.333333334 + x = 2.147349789

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 2.147349789 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.147349789 + -2.333333334
x = 2.147349789 + -2.333333334

Combine like terms: 2.147349789 + -2.333333334 = -0.185983545
x = -0.185983545

Simplifying
x = -0.185983545


Subproblem 2
x + 2.333333334 = -2.147349789

Simplifying
x + 2.333333334 = -2.147349789

Reorder the terms:
2.333333334 + x = -2.147349789

Solving
2.333333334 + x = -2.147349789

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -2.147349789 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.147349789 + -2.333333334
x = -2.147349789 + -2.333333334

Combine like terms: -2.147349789 + -2.333333334 = -4.480683123
x = -4.480683123

Simplifying
x = -4.480683123


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.185983545, -4.480683123}

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