7x^2+3x-56=0

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Solution for 7x^2+3x-56=0 equation: 


Simplifying
7x2 + 3x + -56 = 0

Reorder the terms:
-56 + 3x + 7x2 = 0

Solving
-56 + 3x + 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'.
-8 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 0.4285714286x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 0.4285714286x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 0.4285714286x + x2 = 0 + 8
0.4285714286x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
0.4285714286x + x2 = 8

The x term is 0.4285714286x.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286x + 0.04591836735 + x2 = 8 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 8 + 0.04591836735

Combine like terms: 8 + 0.04591836735 = 8.04591836735
0.04591836735 + 0.4285714286x + x2 = 8.04591836735

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 8.04591836735

Calculate the square root of the right side: 2.836532807

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 2.836532807 and -2.836532807.


Subproblem 1
x + 0.2142857143 = 2.836532807

Simplifying
x + 0.2142857143 = 2.836532807

Reorder the terms:
0.2142857143 + x = 2.836532807

Solving
0.2142857143 + x = 2.836532807

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = 2.836532807 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 2.836532807 + -0.2142857143
x = 2.836532807 + -0.2142857143

Combine like terms: 2.836532807 + -0.2142857143 = 2.6222470927
x = 2.6222470927

Simplifying
x = 2.6222470927


Subproblem 2
x + 0.2142857143 = -2.836532807

Simplifying
x + 0.2142857143 = -2.836532807

Reorder the terms:
0.2142857143 + x = -2.836532807

Solving
0.2142857143 + x = -2.836532807

Solving for variable 'x'.

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

Add '-0.2142857143' to each side of the equation.
0.2142857143 + -0.2142857143 + x = -2.836532807 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -2.836532807 + -0.2142857143
x = -2.836532807 + -0.2142857143

Combine like terms: -2.836532807 + -0.2142857143 = -3.0508185213
x = -3.0508185213

Simplifying
x = -3.0508185213


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6222470927, -3.0508185213}

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