7x^2-40x+45=0

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Solution for 7x^2-40x+45=0 equation: 


Simplifying
7x2 + -40x + 45 = 0

Reorder the terms:
45 + -40x + 7x2 = 0

Solving
45 + -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'.
6.428571429 + -5.714285714x + x2 = 0

Move the constant term to the right:

Add '-6.428571429' to each side of the equation.
6.428571429 + -5.714285714x + -6.428571429 + x2 = 0 + -6.428571429

Reorder the terms:
6.428571429 + -6.428571429 + -5.714285714x + x2 = 0 + -6.428571429

Combine like terms: 6.428571429 + -6.428571429 = 0.000000000
0.000000000 + -5.714285714x + x2 = 0 + -6.428571429
-5.714285714x + x2 = 0 + -6.428571429

Combine like terms: 0 + -6.428571429 = -6.428571429
-5.714285714x + x2 = -6.428571429

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 = -6.428571429 + 8.163265305

Reorder the terms:
8.163265305 + -5.714285714x + x2 = -6.428571429 + 8.163265305

Combine like terms: -6.428571429 + 8.163265305 = 1.734693876
8.163265305 + -5.714285714x + x2 = 1.734693876

Factor a perfect square on the left side:
(x + -2.857142857)(x + -2.857142857) = 1.734693876

Calculate the square root of the right side: 1.317077779

Break this problem into two subproblems by setting 
(x + -2.857142857) equal to 1.317077779 and -1.317077779.


Subproblem 1
x + -2.857142857 = 1.317077779

Simplifying
x + -2.857142857 = 1.317077779

Reorder the terms:
-2.857142857 + x = 1.317077779

Solving
-2.857142857 + x = 1.317077779

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 = 1.317077779 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = 1.317077779 + 2.857142857
x = 1.317077779 + 2.857142857

Combine like terms: 1.317077779 + 2.857142857 = 4.174220636
x = 4.174220636

Simplifying
x = 4.174220636


Subproblem 2
x + -2.857142857 = -1.317077779

Simplifying
x + -2.857142857 = -1.317077779

Reorder the terms:
-2.857142857 + x = -1.317077779

Solving
-2.857142857 + x = -1.317077779

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 = -1.317077779 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + x = -1.317077779 + 2.857142857
x = -1.317077779 + 2.857142857

Combine like terms: -1.317077779 + 2.857142857 = 1.540065078
x = 1.540065078

Simplifying
x = 1.540065078


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.174220636, 1.540065078}

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