x^2-7x+0.75=0

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Solution for x^2-7x+0.75=0 equation: 


Simplifying
x2 + -7x + 0.75 = 0

Reorder the terms:
0.75 + -7x + x2 = 0

Solving
0.75 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + -7x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + -7x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + -7x + x2 = 0 + -0.75
-7x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
-7x + x2 = -0.75

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = -0.75 + 12.25

Reorder the terms:
12.25 + -7x + x2 = -0.75 + 12.25

Combine like terms: -0.75 + 12.25 = 11.5
12.25 + -7x + x2 = 11.5

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.391164992 and -3.391164992.


Subproblem 1
x + -3.5 = 3.391164992

Simplifying
x + -3.5 = 3.391164992

Reorder the terms:
-3.5 + x = 3.391164992

Solving
-3.5 + x = 3.391164992

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.391164992 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.391164992 + 3.5
x = 3.391164992 + 3.5

Combine like terms: 3.391164992 + 3.5 = 6.891164992
x = 6.891164992

Simplifying
x = 6.891164992


Subproblem 2
x + -3.5 = -3.391164992

Simplifying
x + -3.5 = -3.391164992

Reorder the terms:
-3.5 + x = -3.391164992

Solving
-3.5 + x = -3.391164992

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.391164992 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.391164992 + 3.5
x = -3.391164992 + 3.5

Combine like terms: -3.391164992 + 3.5 = 0.108835008
x = 0.108835008

Simplifying
x = 0.108835008


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.891164992, 0.108835008}

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