2x^2-70x-600=0

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Solution for 2x^2-70x-600=0 equation: 


Simplifying
2x2 + -70x + -600 = 0

Reorder the terms:
-600 + -70x + 2x2 = 0

Solving
-600 + -70x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-300 + -35x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-300 + -35x + x2)' equal to zero and attempt to solve:

Simplifying
-300 + -35x + x2 = 0

Solving
-300 + -35x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '300' to each side of the equation.
-300 + -35x + 300 + x2 = 0 + 300

Reorder the terms:
-300 + 300 + -35x + x2 = 0 + 300

Combine like terms: -300 + 300 = 0
0 + -35x + x2 = 0 + 300
-35x + x2 = 0 + 300

Combine like terms: 0 + 300 = 300
-35x + x2 = 300

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = 300 + 306.25

Reorder the terms:
306.25 + -35x + x2 = 300 + 306.25

Combine like terms: 300 + 306.25 = 606.25
306.25 + -35x + x2 = 606.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 606.25

Calculate the square root of the right side: 24.622144504

Break this problem into two subproblems by setting 
(x + -17.5) equal to 24.622144504 and -24.622144504.


Subproblem 1
x + -17.5 = 24.622144504

Simplifying
x + -17.5 = 24.622144504

Reorder the terms:
-17.5 + x = 24.622144504

Solving
-17.5 + x = 24.622144504

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = 24.622144504 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = 24.622144504 + 17.5
x = 24.622144504 + 17.5

Combine like terms: 24.622144504 + 17.5 = 42.122144504
x = 42.122144504

Simplifying
x = 42.122144504


Subproblem 2
x + -17.5 = -24.622144504

Simplifying
x + -17.5 = -24.622144504

Reorder the terms:
-17.5 + x = -24.622144504

Solving
-17.5 + x = -24.622144504

Solving for variable 'x'.

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

Add '17.5' to each side of the equation.
-17.5 + 17.5 + x = -24.622144504 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + x = -24.622144504 + 17.5
x = -24.622144504 + 17.5

Combine like terms: -24.622144504 + 17.5 = -7.122144504
x = -7.122144504

Simplifying
x = -7.122144504


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {42.122144504, -7.122144504}
Solution
x = {42.122144504, -7.122144504}

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