x^2-7x-4.25=0

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Solution for x^2-7x-4.25=0 equation: 


Simplifying
x2 + -7x + -4.25 = 0

Reorder the terms:
-4.25 + -7x + x2 = 0

Solving
-4.25 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -7x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + -7x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -7x + x2 = 0 + 4.25
-7x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
-7x + x2 = 4.25

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 = 4.25 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 4.25 + 12.25

Combine like terms: 4.25 + 12.25 = 16.5
12.25 + -7x + x2 = 16.5

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 16.5

Calculate the square root of the right side: 4.062019202

Break this problem into two subproblems by setting 
(x + -3.5) equal to 4.062019202 and -4.062019202.


Subproblem 1
x + -3.5 = 4.062019202

Simplifying
x + -3.5 = 4.062019202

Reorder the terms:
-3.5 + x = 4.062019202

Solving
-3.5 + x = 4.062019202

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 = 4.062019202 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 4.062019202 + 3.5
x = 4.062019202 + 3.5

Combine like terms: 4.062019202 + 3.5 = 7.562019202
x = 7.562019202

Simplifying
x = 7.562019202


Subproblem 2
x + -3.5 = -4.062019202

Simplifying
x + -3.5 = -4.062019202

Reorder the terms:
-3.5 + x = -4.062019202

Solving
-3.5 + x = -4.062019202

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 = -4.062019202 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -4.062019202 + 3.5
x = -4.062019202 + 3.5

Combine like terms: -4.062019202 + 3.5 = -0.562019202
x = -0.562019202

Simplifying
x = -0.562019202


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.562019202, -0.562019202}

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