7x^2-40x+13=0

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Solution for 7x^2-40x+13=0 equation: 


Simplifying
7x2 + -40x + 13 = 0

Reorder the terms:
13 + -40x + 7x2 = 0

Solving
13 + -40x + 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'.
1.857142857 + -5.714285714x + x2 = 0

Move the constant term to the right:

Add '-1.857142857' to each side of the equation.
1.857142857 + -5.714285714x + -1.857142857 + x2 = 0 + -1.857142857

Reorder the terms:
1.857142857 + -1.857142857 + -5.714285714x + x2 = 0 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + -5.714285714x + x2 = 0 + -1.857142857
-5.714285714x + x2 = 0 + -1.857142857

Combine like terms: 0 + -1.857142857 = -1.857142857
-5.714285714x + x2 = -1.857142857

The x term is -5.714285714x.  Take half its coefficient (-2.857142857).
Square it (8.163265305) and add it to both sides.

Add '8.163265305' to each side of the equation.
-5.714285714x + 8.163265305 + x2 = -1.857142857 + 8.163265305

Reorder the terms:
8.163265305 + -5.714285714x + x2 = -1.857142857 + 8.163265305

Combine like terms: -1.857142857 + 8.163265305 = 6.306122448
8.163265305 + -5.714285714x + x2 = 6.306122448

Factor a perfect square on the left side:
(x + -2.857142857)(x + -2.857142857) = 6.306122448

Calculate the square root of the right side: 2.511199404

Break this problem into two subproblems by setting 
(x + -2.857142857) equal to 2.511199404 and -2.511199404.


Subproblem 1
x + -2.857142857 = 2.511199404

Simplifying
x + -2.857142857 = 2.511199404

Reorder the terms:
-2.857142857 + x = 2.511199404

Solving
-2.857142857 + x = 2.511199404

Solving for variable 'x'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + x = 2.511199404 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = 2.511199404 + 2.857142857
x = 2.511199404 + 2.857142857

Combine like terms: 2.511199404 + 2.857142857 = 5.368342261
x = 5.368342261

Simplifying
x = 5.368342261


Subproblem 2
x + -2.857142857 = -2.511199404

Simplifying
x + -2.857142857 = -2.511199404

Reorder the terms:
-2.857142857 + x = -2.511199404

Solving
-2.857142857 + x = -2.511199404

Solving for variable 'x'.

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

Add '2.857142857' to each side of the equation.
-2.857142857 + 2.857142857 + x = -2.511199404 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = -2.511199404 + 2.857142857
x = -2.511199404 + 2.857142857

Combine like terms: -2.511199404 + 2.857142857 = 0.345943453
x = 0.345943453

Simplifying
x = 0.345943453


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.368342261, 0.345943453}

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