x^2-11x-70=0

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Solution for x^2-11x-70=0 equation: 


Simplifying
x2 + -11x + -70 = 0

Reorder the terms:
-70 + -11x + x2 = 0

Solving
-70 + -11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + -11x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -11x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -11x + x2 = 0 + 70
-11x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-11x + x2 = 70

The x term is -11x.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11x + 30.25 + x2 = 70 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 70 + 30.25

Combine like terms: 70 + 30.25 = 100.25
30.25 + -11x + x2 = 100.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + -5.5) equal to 10.012492197 and -10.012492197.


Subproblem 1
x + -5.5 = 10.012492197

Simplifying
x + -5.5 = 10.012492197

Reorder the terms:
-5.5 + x = 10.012492197

Solving
-5.5 + x = 10.012492197

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = 10.012492197 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 10.012492197 + 5.5
x = 10.012492197 + 5.5

Combine like terms: 10.012492197 + 5.5 = 15.512492197
x = 15.512492197

Simplifying
x = 15.512492197


Subproblem 2
x + -5.5 = -10.012492197

Simplifying
x + -5.5 = -10.012492197

Reorder the terms:
-5.5 + x = -10.012492197

Solving
-5.5 + x = -10.012492197

Solving for variable 'x'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + x = -10.012492197 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -10.012492197 + 5.5
x = -10.012492197 + 5.5

Combine like terms: -10.012492197 + 5.5 = -4.512492197
x = -4.512492197

Simplifying
x = -4.512492197


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.512492197, -4.512492197}

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