x^2-7x-70=0

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Solution for x^2-7x-70=0 equation: 


Simplifying
x2 + -7x + -70 = 0

Reorder the terms:
-70 + -7x + x2 = 0

Solving
-70 + -7x + 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 + -7x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -7x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -7x + x2 = 0 + 70
-7x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-7x + x2 = 70

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 = 70 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 70 + 12.25

Combine like terms: 70 + 12.25 = 82.25
12.25 + -7x + x2 = 82.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(x + -3.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
x + -3.5 = 9.069178574

Simplifying
x + -3.5 = 9.069178574

Reorder the terms:
-3.5 + x = 9.069178574

Solving
-3.5 + x = 9.069178574

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 = 9.069178574 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 9.069178574 + 3.5
x = 9.069178574 + 3.5

Combine like terms: 9.069178574 + 3.5 = 12.569178574
x = 12.569178574

Simplifying
x = 12.569178574


Subproblem 2
x + -3.5 = -9.069178574

Simplifying
x + -3.5 = -9.069178574

Reorder the terms:
-3.5 + x = -9.069178574

Solving
-3.5 + x = -9.069178574

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 = -9.069178574 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -9.069178574 + 3.5
x = -9.069178574 + 3.5

Combine like terms: -9.069178574 + 3.5 = -5.569178574
x = -5.569178574

Simplifying
x = -5.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.569178574, -5.569178574}

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