7x^2+8x-4=0

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Solution for 7x^2+8x-4=0 equation: 


Simplifying
7x2 + 8x + -4 = 0

Reorder the terms:
-4 + 8x + 7x2 = 0

Solving
-4 + 8x + 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'.
-0.5714285714 + 1.142857143x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 1.142857143x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 1.142857143x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 1.142857143x + x2 = 0 + 0.5714285714
1.142857143x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
1.142857143x + x2 = 0.5714285714

The x term is 1.142857143x.  Take half its coefficient (0.5714285715).
Square it (0.3265306123) and add it to both sides.

Add '0.3265306123' to each side of the equation.
1.142857143x + 0.3265306123 + x2 = 0.5714285714 + 0.3265306123

Reorder the terms:
0.3265306123 + 1.142857143x + x2 = 0.5714285714 + 0.3265306123

Combine like terms: 0.5714285714 + 0.3265306123 = 0.8979591837
0.3265306123 + 1.142857143x + x2 = 0.8979591837

Factor a perfect square on the left side:
(x + 0.5714285715)(x + 0.5714285715) = 0.8979591837

Calculate the square root of the right side: 0.947607083

Break this problem into two subproblems by setting 
(x + 0.5714285715) equal to 0.947607083 and -0.947607083.


Subproblem 1
x + 0.5714285715 = 0.947607083

Simplifying
x + 0.5714285715 = 0.947607083

Reorder the terms:
0.5714285715 + x = 0.947607083

Solving
0.5714285715 + x = 0.947607083

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = 0.947607083 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = 0.947607083 + -0.5714285715
x = 0.947607083 + -0.5714285715

Combine like terms: 0.947607083 + -0.5714285715 = 0.3761785115
x = 0.3761785115

Simplifying
x = 0.3761785115


Subproblem 2
x + 0.5714285715 = -0.947607083

Simplifying
x + 0.5714285715 = -0.947607083

Reorder the terms:
0.5714285715 + x = -0.947607083

Solving
0.5714285715 + x = -0.947607083

Solving for variable 'x'.

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

Add '-0.5714285715' to each side of the equation.
0.5714285715 + -0.5714285715 + x = -0.947607083 + -0.5714285715

Combine like terms: 0.5714285715 + -0.5714285715 = 0.0000000000
0.0000000000 + x = -0.947607083 + -0.5714285715
x = -0.947607083 + -0.5714285715

Combine like terms: -0.947607083 + -0.5714285715 = -1.5190356545
x = -1.5190356545

Simplifying
x = -1.5190356545


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3761785115, -1.5190356545}

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