2x^2-11x-70=0

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Solution for 2x^2-11x-70=0 equation: 


Simplifying
2x2 + -11x + -70 = 0

Reorder the terms:
-70 + -11x + 2x2 = 0

Solving
-70 + -11x + 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 + -5.5x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -5.5x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + -5.5x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -5.5x + x2 = 0 + 35
-5.5x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
-5.5x + x2 = 35

The x term is -5.5x.  Take half its coefficient (-2.75).
Square it (7.5625) and add it to both sides.

Add '7.5625' to each side of the equation.
-5.5x + 7.5625 + x2 = 35 + 7.5625

Reorder the terms:
7.5625 + -5.5x + x2 = 35 + 7.5625

Combine like terms: 35 + 7.5625 = 42.5625
7.5625 + -5.5x + x2 = 42.5625

Factor a perfect square on the left side:
(x + -2.75)(x + -2.75) = 42.5625

Calculate the square root of the right side: 6.523994175

Break this problem into two subproblems by setting 
(x + -2.75) equal to 6.523994175 and -6.523994175.


Subproblem 1
x + -2.75 = 6.523994175

Simplifying
x + -2.75 = 6.523994175

Reorder the terms:
-2.75 + x = 6.523994175

Solving
-2.75 + x = 6.523994175

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = 6.523994175 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = 6.523994175 + 2.75
x = 6.523994175 + 2.75

Combine like terms: 6.523994175 + 2.75 = 9.273994175
x = 9.273994175

Simplifying
x = 9.273994175


Subproblem 2
x + -2.75 = -6.523994175

Simplifying
x + -2.75 = -6.523994175

Reorder the terms:
-2.75 + x = -6.523994175

Solving
-2.75 + x = -6.523994175

Solving for variable 'x'.

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

Add '2.75' to each side of the equation.
-2.75 + 2.75 + x = -6.523994175 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + x = -6.523994175 + 2.75
x = -6.523994175 + 2.75

Combine like terms: -6.523994175 + 2.75 = -3.773994175
x = -3.773994175

Simplifying
x = -3.773994175


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.273994175, -3.773994175}

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