7x^2+57x-12=0

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Solution for 7x^2+57x-12=0 equation: 


Simplifying
7x2 + 57x + -12 = 0

Reorder the terms:
-12 + 57x + 7x2 = 0

Solving
-12 + 57x + 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'.
-1.714285714 + 8.142857143x + x2 = 0

Move the constant term to the right:

Add '1.714285714' to each side of the equation.
-1.714285714 + 8.142857143x + 1.714285714 + x2 = 0 + 1.714285714

Reorder the terms:
-1.714285714 + 1.714285714 + 8.142857143x + x2 = 0 + 1.714285714

Combine like terms: -1.714285714 + 1.714285714 = 0.000000000
0.000000000 + 8.142857143x + x2 = 0 + 1.714285714
8.142857143x + x2 = 0 + 1.714285714

Combine like terms: 0 + 1.714285714 = 1.714285714
8.142857143x + x2 = 1.714285714

The x term is 8.142857143x.  Take half its coefficient (4.071428572).
Square it (16.57653062) and add it to both sides.

Add '16.57653062' to each side of the equation.
8.142857143x + 16.57653062 + x2 = 1.714285714 + 16.57653062

Reorder the terms:
16.57653062 + 8.142857143x + x2 = 1.714285714 + 16.57653062

Combine like terms: 1.714285714 + 16.57653062 = 18.290816334
16.57653062 + 8.142857143x + x2 = 18.290816334

Factor a perfect square on the left side:
(x + 4.071428572)(x + 4.071428572) = 18.290816334

Calculate the square root of the right side: 4.276776395

Break this problem into two subproblems by setting 
(x + 4.071428572) equal to 4.276776395 and -4.276776395.


Subproblem 1
x + 4.071428572 = 4.276776395

Simplifying
x + 4.071428572 = 4.276776395

Reorder the terms:
4.071428572 + x = 4.276776395

Solving
4.071428572 + x = 4.276776395

Solving for variable 'x'.

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

Add '-4.071428572' to each side of the equation.
4.071428572 + -4.071428572 + x = 4.276776395 + -4.071428572

Combine like terms: 4.071428572 + -4.071428572 = 0.000000000
0.000000000 + x = 4.276776395 + -4.071428572
x = 4.276776395 + -4.071428572

Combine like terms: 4.276776395 + -4.071428572 = 0.205347823
x = 0.205347823

Simplifying
x = 0.205347823


Subproblem 2
x + 4.071428572 = -4.276776395

Simplifying
x + 4.071428572 = -4.276776395

Reorder the terms:
4.071428572 + x = -4.276776395

Solving
4.071428572 + x = -4.276776395

Solving for variable 'x'.

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

Add '-4.071428572' to each side of the equation.
4.071428572 + -4.071428572 + x = -4.276776395 + -4.071428572

Combine like terms: 4.071428572 + -4.071428572 = 0.000000000
0.000000000 + x = -4.276776395 + -4.071428572
x = -4.276776395 + -4.071428572

Combine like terms: -4.276776395 + -4.071428572 = -8.348204967
x = -8.348204967

Simplifying
x = -8.348204967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.205347823, -8.348204967}

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