x^2-7x-293=0

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Solution for x^2-7x-293=0 equation: 


Simplifying
x2 + -7x + -293 = 0

Reorder the terms:
-293 + -7x + x2 = 0

Solving
-293 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '293' to each side of the equation.
-293 + -7x + 293 + x2 = 0 + 293

Reorder the terms:
-293 + 293 + -7x + x2 = 0 + 293

Combine like terms: -293 + 293 = 0
0 + -7x + x2 = 0 + 293
-7x + x2 = 0 + 293

Combine like terms: 0 + 293 = 293
-7x + x2 = 293

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 = 293 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 293 + 12.25

Combine like terms: 293 + 12.25 = 305.25
12.25 + -7x + x2 = 305.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 305.25

Calculate the square root of the right side: 17.47140521

Break this problem into two subproblems by setting 
(x + -3.5) equal to 17.47140521 and -17.47140521.


Subproblem 1
x + -3.5 = 17.47140521

Simplifying
x + -3.5 = 17.47140521

Reorder the terms:
-3.5 + x = 17.47140521

Solving
-3.5 + x = 17.47140521

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 = 17.47140521 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 17.47140521 + 3.5
x = 17.47140521 + 3.5

Combine like terms: 17.47140521 + 3.5 = 20.97140521
x = 20.97140521

Simplifying
x = 20.97140521


Subproblem 2
x + -3.5 = -17.47140521

Simplifying
x + -3.5 = -17.47140521

Reorder the terms:
-3.5 + x = -17.47140521

Solving
-3.5 + x = -17.47140521

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 = -17.47140521 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -17.47140521 + 3.5
x = -17.47140521 + 3.5

Combine like terms: -17.47140521 + 3.5 = -13.97140521
x = -13.97140521

Simplifying
x = -13.97140521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.97140521, -13.97140521}

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