x^2-30x-70=0

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Solution for x^2-30x-70=0 equation: 


Simplifying
x2 + -30x + -70 = 0

Reorder the terms:
-70 + -30x + x2 = 0

Solving
-70 + -30x + 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 + -30x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + -30x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + -30x + x2 = 0 + 70
-30x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
-30x + x2 = 70

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 70 + 225

Reorder the terms:
225 + -30x + x2 = 70 + 225

Combine like terms: 70 + 225 = 295
225 + -30x + x2 = 295

Factor a perfect square on the left side:
(x + -15)(x + -15) = 295

Calculate the square root of the right side: 17.175564037

Break this problem into two subproblems by setting 
(x + -15) equal to 17.175564037 and -17.175564037.


Subproblem 1
x + -15 = 17.175564037

Simplifying
x + -15 = 17.175564037

Reorder the terms:
-15 + x = 17.175564037

Solving
-15 + x = 17.175564037

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 17.175564037 + 15

Combine like terms: -15 + 15 = 0
0 + x = 17.175564037 + 15
x = 17.175564037 + 15

Combine like terms: 17.175564037 + 15 = 32.175564037
x = 32.175564037

Simplifying
x = 32.175564037


Subproblem 2
x + -15 = -17.175564037

Simplifying
x + -15 = -17.175564037

Reorder the terms:
-15 + x = -17.175564037

Solving
-15 + x = -17.175564037

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -17.175564037 + 15

Combine like terms: -15 + 15 = 0
0 + x = -17.175564037 + 15
x = -17.175564037 + 15

Combine like terms: -17.175564037 + 15 = -2.175564037
x = -2.175564037

Simplifying
x = -2.175564037


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.175564037, -2.175564037}

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