3x^2+7x=49

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Solution for 3x^2+7x=49 equation: 


Simplifying
3x2 + 7x = 49

Reorder the terms:
7x + 3x2 = 49

Solving
7x + 3x2 = 49

Solving for variable 'x'.

Reorder the terms:
-49 + 7x + 3x2 = 49 + -49

Combine like terms: 49 + -49 = 0
-49 + 7x + 3x2 = 0

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

Divide each side by '3'.
-16.33333333 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + 2.333333333x + 16.33333333 + x2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + 2.333333333x + x2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + 2.333333333x + x2 = 0 + 16.33333333
2.333333333x + x2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
2.333333333x + x2 = 16.33333333

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 16.33333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 16.33333333 + 1.361111112

Combine like terms: 16.33333333 + 1.361111112 = 17.694444442
1.361111112 + 2.333333333x + x2 = 17.694444442

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 17.694444442

Calculate the square root of the right side: 4.206476488

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 4.206476488 and -4.206476488.


Subproblem 1
x + 1.166666667 = 4.206476488

Simplifying
x + 1.166666667 = 4.206476488

Reorder the terms:
1.166666667 + x = 4.206476488

Solving
1.166666667 + x = 4.206476488

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 4.206476488 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 4.206476488 + -1.166666667
x = 4.206476488 + -1.166666667

Combine like terms: 4.206476488 + -1.166666667 = 3.039809821
x = 3.039809821

Simplifying
x = 3.039809821


Subproblem 2
x + 1.166666667 = -4.206476488

Simplifying
x + 1.166666667 = -4.206476488

Reorder the terms:
1.166666667 + x = -4.206476488

Solving
1.166666667 + x = -4.206476488

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -4.206476488 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -4.206476488 + -1.166666667
x = -4.206476488 + -1.166666667

Combine like terms: -4.206476488 + -1.166666667 = -5.373143155
x = -5.373143155

Simplifying
x = -5.373143155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.039809821, -5.373143155}

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