x^2+14x-70=0

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Solution for x^2+14x-70=0 equation: 


Simplifying
x2 + 14x + -70 = 0

Reorder the terms:
-70 + 14x + x2 = 0

Solving
-70 + 14x + 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 + 14x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 14x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 14x + x2 = 0 + 70
14x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
14x + x2 = 70

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 70 + 49

Reorder the terms:
49 + 14x + x2 = 70 + 49

Combine like terms: 70 + 49 = 119
49 + 14x + x2 = 119

Factor a perfect square on the left side:
(x + 7)(x + 7) = 119

Calculate the square root of the right side: 10.908712115

Break this problem into two subproblems by setting 
(x + 7) equal to 10.908712115 and -10.908712115.


Subproblem 1
x + 7 = 10.908712115

Simplifying
x + 7 = 10.908712115

Reorder the terms:
7 + x = 10.908712115

Solving
7 + x = 10.908712115

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 10.908712115 + -7

Combine like terms: 7 + -7 = 0
0 + x = 10.908712115 + -7
x = 10.908712115 + -7

Combine like terms: 10.908712115 + -7 = 3.908712115
x = 3.908712115

Simplifying
x = 3.908712115


Subproblem 2
x + 7 = -10.908712115

Simplifying
x + 7 = -10.908712115

Reorder the terms:
7 + x = -10.908712115

Solving
7 + x = -10.908712115

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -10.908712115 + -7

Combine like terms: 7 + -7 = 0
0 + x = -10.908712115 + -7
x = -10.908712115 + -7

Combine like terms: -10.908712115 + -7 = -17.908712115
x = -17.908712115

Simplifying
x = -17.908712115


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.908712115, -17.908712115}

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