7x^2+35x-9=0

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Solution for 7x^2+35x-9=0 equation: 


Simplifying
7x2 + 35x + -9 = 0

Reorder the terms:
-9 + 35x + 7x2 = 0

Solving
-9 + 35x + 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'.
-1.285714286 + 5x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + 5x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + 5x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + 5x + x2 = 0 + 1.285714286
5x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
5x + x2 = 1.285714286

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 1.285714286 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1.285714286 + 6.25

Combine like terms: 1.285714286 + 6.25 = 7.535714286
6.25 + 5x + x2 = 7.535714286

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 7.535714286

Calculate the square root of the right side: 2.74512555

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.74512555 and -2.74512555.


Subproblem 1
x + 2.5 = 2.74512555

Simplifying
x + 2.5 = 2.74512555

Reorder the terms:
2.5 + x = 2.74512555

Solving
2.5 + x = 2.74512555

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.74512555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.74512555 + -2.5
x = 2.74512555 + -2.5

Combine like terms: 2.74512555 + -2.5 = 0.24512555
x = 0.24512555

Simplifying
x = 0.24512555


Subproblem 2
x + 2.5 = -2.74512555

Simplifying
x + 2.5 = -2.74512555

Reorder the terms:
2.5 + x = -2.74512555

Solving
2.5 + x = -2.74512555

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.74512555 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.74512555 + -2.5
x = -2.74512555 + -2.5

Combine like terms: -2.74512555 + -2.5 = -5.24512555
x = -5.24512555

Simplifying
x = -5.24512555


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.24512555, -5.24512555}

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