7x^2+22x-4=0

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Solution for 7x^2+22x-4=0 equation: 


Simplifying
7x2 + 22x + -4 = 0

Reorder the terms:
-4 + 22x + 7x2 = 0

Solving
-4 + 22x + 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 + 3.142857143x + x2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 3.142857143x + 0.5714285714 + x2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 3.142857143x + x2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 3.142857143x + x2 = 0 + 0.5714285714
3.142857143x + x2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
3.142857143x + x2 = 0.5714285714

The x term is 3.142857143x.  Take half its coefficient (1.571428572).
Square it (2.469387757) and add it to both sides.

Add '2.469387757' to each side of the equation.
3.142857143x + 2.469387757 + x2 = 0.5714285714 + 2.469387757

Reorder the terms:
2.469387757 + 3.142857143x + x2 = 0.5714285714 + 2.469387757

Combine like terms: 0.5714285714 + 2.469387757 = 3.0408163284
2.469387757 + 3.142857143x + x2 = 3.0408163284

Factor a perfect square on the left side:
(x + 1.571428572)(x + 1.571428572) = 3.0408163284

Calculate the square root of the right side: 1.74379366

Break this problem into two subproblems by setting 
(x + 1.571428572) equal to 1.74379366 and -1.74379366.


Subproblem 1
x + 1.571428572 = 1.74379366

Simplifying
x + 1.571428572 = 1.74379366

Reorder the terms:
1.571428572 + x = 1.74379366

Solving
1.571428572 + x = 1.74379366

Solving for variable 'x'.

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

Add '-1.571428572' to each side of the equation.
1.571428572 + -1.571428572 + x = 1.74379366 + -1.571428572

Combine like terms: 1.571428572 + -1.571428572 = 0.000000000
0.000000000 + x = 1.74379366 + -1.571428572
x = 1.74379366 + -1.571428572

Combine like terms: 1.74379366 + -1.571428572 = 0.172365088
x = 0.172365088

Simplifying
x = 0.172365088


Subproblem 2
x + 1.571428572 = -1.74379366

Simplifying
x + 1.571428572 = -1.74379366

Reorder the terms:
1.571428572 + x = -1.74379366

Solving
1.571428572 + x = -1.74379366

Solving for variable 'x'.

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

Add '-1.571428572' to each side of the equation.
1.571428572 + -1.571428572 + x = -1.74379366 + -1.571428572

Combine like terms: 1.571428572 + -1.571428572 = 0.000000000
0.000000000 + x = -1.74379366 + -1.571428572
x = -1.74379366 + -1.571428572

Combine like terms: -1.74379366 + -1.571428572 = -3.315222232
x = -3.315222232

Simplifying
x = -3.315222232


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.172365088, -3.315222232}

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