7x^2+50x+27=0

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Solution for 7x^2+50x+27=0 equation: 


Simplifying
7x2 + 50x + 27 = 0

Reorder the terms:
27 + 50x + 7x2 = 0

Solving
27 + 50x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
3.857142857 + 7.142857143x + x2 = 0

Move the constant term to the right:

Add '-3.857142857' to each side of the equation.
3.857142857 + 7.142857143x + -3.857142857 + x2 = 0 + -3.857142857

Reorder the terms:
3.857142857 + -3.857142857 + 7.142857143x + x2 = 0 + -3.857142857

Combine like terms: 3.857142857 + -3.857142857 = 0.000000000
0.000000000 + 7.142857143x + x2 = 0 + -3.857142857
7.142857143x + x2 = 0 + -3.857142857

Combine like terms: 0 + -3.857142857 = -3.857142857
7.142857143x + x2 = -3.857142857

The x term is 7.142857143x.  Take half its coefficient (3.571428572).
Square it (12.75510204) and add it to both sides.

Add '12.75510204' to each side of the equation.
7.142857143x + 12.75510204 + x2 = -3.857142857 + 12.75510204

Reorder the terms:
12.75510204 + 7.142857143x + x2 = -3.857142857 + 12.75510204

Combine like terms: -3.857142857 + 12.75510204 = 8.897959183
12.75510204 + 7.142857143x + x2 = 8.897959183

Factor a perfect square on the left side:
(x + 3.571428572)(x + 3.571428572) = 8.897959183

Calculate the square root of the right side: 2.982944717

Break this problem into two subproblems by setting 
(x + 3.571428572) equal to 2.982944717 and -2.982944717.


Subproblem 1
x + 3.571428572 = 2.982944717

Simplifying
x + 3.571428572 = 2.982944717

Reorder the terms:
3.571428572 + x = 2.982944717

Solving
3.571428572 + x = 2.982944717

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = 2.982944717 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = 2.982944717 + -3.571428572
x = 2.982944717 + -3.571428572

Combine like terms: 2.982944717 + -3.571428572 = -0.588483855
x = -0.588483855

Simplifying
x = -0.588483855


Subproblem 2
x + 3.571428572 = -2.982944717

Simplifying
x + 3.571428572 = -2.982944717

Reorder the terms:
3.571428572 + x = -2.982944717

Solving
3.571428572 + x = -2.982944717

Solving for variable 'x'.

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

Add '-3.571428572' to each side of the equation.
3.571428572 + -3.571428572 + x = -2.982944717 + -3.571428572

Combine like terms: 3.571428572 + -3.571428572 = 0.000000000
0.000000000 + x = -2.982944717 + -3.571428572
x = -2.982944717 + -3.571428572

Combine like terms: -2.982944717 + -3.571428572 = -6.554373289
x = -6.554373289

Simplifying
x = -6.554373289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.588483855, -6.554373289}

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