x^2-7x=0.75

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


Simplifying
x2 + -7x = 0.75

Reorder the terms:
-7x + x2 = 0.75

Solving
-7x + x2 = 0.75

Solving for variable 'x'.

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

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

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 = 0.00 + 0.75

Reorder the terms:
-0.75 + 0.75 + -7x + x2 = 0.00 + 0.75

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

Combine like terms: 0.00 + 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 = 13
12.25 + -7x + x2 = 13

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -3.5 = 3.605551275

Simplifying
x + -3.5 = 3.605551275

Reorder the terms:
-3.5 + x = 3.605551275

Solving
-3.5 + x = 3.605551275

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 = 3.605551275 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.605551275 + 3.5
x = 3.605551275 + 3.5

Combine like terms: 3.605551275 + 3.5 = 7.105551275
x = 7.105551275

Simplifying
x = 7.105551275


Subproblem 2
x + -3.5 = -3.605551275

Simplifying
x + -3.5 = -3.605551275

Reorder the terms:
-3.5 + x = -3.605551275

Solving
-3.5 + x = -3.605551275

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 = -3.605551275 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.605551275 + 3.5
x = -3.605551275 + 3.5

Combine like terms: -3.605551275 + 3.5 = -0.105551275
x = -0.105551275

Simplifying
x = -0.105551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.105551275, -0.105551275}

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