7x^2+3x-9=0

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Solution for 7x^2+3x-9=0 equation: 


Simplifying
7x2 + 3x + -9 = 0

Reorder the terms:
-9 + 3x + 7x2 = 0

Solving
-9 + 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'.
-1.285714286 + 0.4285714286x + x2 = 0

Move the constant term to the right:

Add '1.285714286' to each side of the equation.
-1.285714286 + 0.4285714286x + 1.285714286 + x2 = 0 + 1.285714286

Reorder the terms:
-1.285714286 + 1.285714286 + 0.4285714286x + x2 = 0 + 1.285714286

Combine like terms: -1.285714286 + 1.285714286 = 0.000000000
0.000000000 + 0.4285714286x + x2 = 0 + 1.285714286
0.4285714286x + x2 = 0 + 1.285714286

Combine like terms: 0 + 1.285714286 = 1.285714286
0.4285714286x + x2 = 1.285714286

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 = 1.285714286 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286x + x2 = 1.285714286 + 0.04591836735

Combine like terms: 1.285714286 + 0.04591836735 = 1.33163265335
0.04591836735 + 0.4285714286x + x2 = 1.33163265335

Factor a perfect square on the left side:
(x + 0.2142857143)(x + 0.2142857143) = 1.33163265335

Calculate the square root of the right side: 1.153963887

Break this problem into two subproblems by setting 
(x + 0.2142857143) equal to 1.153963887 and -1.153963887.


Subproblem 1
x + 0.2142857143 = 1.153963887

Simplifying
x + 0.2142857143 = 1.153963887

Reorder the terms:
0.2142857143 + x = 1.153963887

Solving
0.2142857143 + x = 1.153963887

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 = 1.153963887 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = 1.153963887 + -0.2142857143
x = 1.153963887 + -0.2142857143

Combine like terms: 1.153963887 + -0.2142857143 = 0.9396781727
x = 0.9396781727

Simplifying
x = 0.9396781727


Subproblem 2
x + 0.2142857143 = -1.153963887

Simplifying
x + 0.2142857143 = -1.153963887

Reorder the terms:
0.2142857143 + x = -1.153963887

Solving
0.2142857143 + x = -1.153963887

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 = -1.153963887 + -0.2142857143

Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000
0.0000000000 + x = -1.153963887 + -0.2142857143
x = -1.153963887 + -0.2142857143

Combine like terms: -1.153963887 + -0.2142857143 = -1.3682496013
x = -1.3682496013

Simplifying
x = -1.3682496013


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9396781727, -1.3682496013}

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