x^2-14x+45.9375=0

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Solution for x^2-14x+45.9375=0 equation: 


Simplifying
x2 + -14x + 45.9375 = 0

Reorder the terms:
45.9375 + -14x + x2 = 0

Solving
45.9375 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-45.9375' to each side of the equation.
45.9375 + -14x + -45.9375 + x2 = 0 + -45.9375

Reorder the terms:
45.9375 + -45.9375 + -14x + x2 = 0 + -45.9375

Combine like terms: 45.9375 + -45.9375 = 0.0000
0.0000 + -14x + x2 = 0 + -45.9375
-14x + x2 = 0 + -45.9375

Combine like terms: 0 + -45.9375 = -45.9375
-14x + x2 = -45.9375

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -45.9375 + 49

Reorder the terms:
49 + -14x + x2 = -45.9375 + 49

Combine like terms: -45.9375 + 49 = 3.0625
49 + -14x + x2 = 3.0625

Factor a perfect square on the left side:
(x + -7)(x + -7) = 3.0625

Calculate the square root of the right side: 1.75

Break this problem into two subproblems by setting 
(x + -7) equal to 1.75 and -1.75.


Subproblem 1
x + -7 = 1.75

Simplifying
x + -7 = 1.75

Reorder the terms:
-7 + x = 1.75

Solving
-7 + x = 1.75

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 1.75 + 7

Combine like terms: -7 + 7 = 0
0 + x = 1.75 + 7
x = 1.75 + 7

Combine like terms: 1.75 + 7 = 8.75
x = 8.75

Simplifying
x = 8.75


Subproblem 2
x + -7 = -1.75

Simplifying
x + -7 = -1.75

Reorder the terms:
-7 + x = -1.75

Solving
-7 + x = -1.75

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -1.75 + 7

Combine like terms: -7 + 7 = 0
0 + x = -1.75 + 7
x = -1.75 + 7

Combine like terms: -1.75 + 7 = 5.25
x = 5.25

Simplifying
x = 5.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.75, 5.25}

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