2x^2-25x-70=0

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Solution for 2x^2-25x-70=0 equation: 


Simplifying
2x2 + -25x + -70 = 0

Reorder the terms:
-70 + -25x + 2x2 = 0

Solving
-70 + -25x + 2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-35 + -12.5x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -12.5x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -12.5x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -12.5x + x2 = 0 + 35
-12.5x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-12.5x + x2 = 35

The x term is -12.5x.  Take half its coefficient (-6.25).
Square it (39.0625) and add it to both sides.

Add '39.0625' to each side of the equation.
-12.5x + 39.0625 + x2 = 35 + 39.0625

Reorder the terms:
39.0625 + -12.5x + x2 = 35 + 39.0625

Combine like terms: 35 + 39.0625 = 74.0625
39.0625 + -12.5x + x2 = 74.0625

Factor a perfect square on the left side:
(x + -6.25)(x + -6.25) = 74.0625

Calculate the square root of the right side: 8.605957239

Break this problem into two subproblems by setting 
(x + -6.25) equal to 8.605957239 and -8.605957239.


Subproblem 1
x + -6.25 = 8.605957239

Simplifying
x + -6.25 = 8.605957239

Reorder the terms:
-6.25 + x = 8.605957239

Solving
-6.25 + x = 8.605957239

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = 8.605957239 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = 8.605957239 + 6.25
x = 8.605957239 + 6.25

Combine like terms: 8.605957239 + 6.25 = 14.855957239
x = 14.855957239

Simplifying
x = 14.855957239


Subproblem 2
x + -6.25 = -8.605957239

Simplifying
x + -6.25 = -8.605957239

Reorder the terms:
-6.25 + x = -8.605957239

Solving
-6.25 + x = -8.605957239

Solving for variable 'x'.

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

Add '6.25' to each side of the equation.
-6.25 + 6.25 + x = -8.605957239 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + x = -8.605957239 + 6.25
x = -8.605957239 + 6.25

Combine like terms: -8.605957239 + 6.25 = -2.355957239
x = -2.355957239

Simplifying
x = -2.355957239


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.855957239, -2.355957239}

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