(11.0)=(-6.4)x+0.5(9.8)x^2

Solution for (11.0)=(-6.4)x+0.5(9.8)x^2 equation:

Simplifying
(11.0) = (-6.4) * x + 0.5(9.8) * x2
11.0 = (-6.4) * x + 0.5(9.8) * x2

Multiply 0.5 * 9.8
11.0 = -6.4x + 4.9x2

Solving
11.0 = -6.4x + 4.9x2

Solving for variable 'x'.

Reorder the terms:
11.0 + 6.4x + -4.9x2 = -6.4x + 6.4x + 4.9x2 + -4.9x2

Combine like terms: -6.4x + 6.4x = 0.0
11.0 + 6.4x + -4.9x2 = 0.0 + 4.9x2 + -4.9x2
11.0 + 6.4x + -4.9x2 = 4.9x2 + -4.9x2

Combine like terms: 4.9x2 + -4.9x2 = 0.0
11.0 + 6.4x + -4.9x2 = 0.0

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-2.244897959 + -1.306122449x + x2 = 0

Move the constant term to the right:

Add '2.244897959' to each side of the equation.
-2.244897959 + -1.306122449x + 2.244897959 + x2 = 0 + 2.244897959

Reorder the terms:
-2.244897959 + 2.244897959 + -1.306122449x + x2 = 0 + 2.244897959

Combine like terms: -2.244897959 + 2.244897959 = 0.000000000
0.000000000 + -1.306122449x + x2 = 0 + 2.244897959
-1.306122449x + x2 = 0 + 2.244897959

Combine like terms: 0 + 2.244897959 = 2.244897959
-1.306122449x + x2 = 2.244897959

The x term is -1.306122449x.  Take half its coefficient (-0.6530612245).
Square it (0.4264889629) and add it to both sides.

Add '0.4264889629' to each side of the equation.
-1.306122449x + 0.4264889629 + x2 = 2.244897959 + 0.4264889629

Reorder the terms:
0.4264889629 + -1.306122449x + x2 = 2.244897959 + 0.4264889629

Combine like terms: 2.244897959 + 0.4264889629 = 2.6713869219
0.4264889629 + -1.306122449x + x2 = 2.6713869219

Factor a perfect square on the left side:
(x + -0.6530612245)(x + -0.6530612245) = 2.6713869219

Calculate the square root of the right side: 1.6344378

Break this problem into two subproblems by setting 
(x + -0.6530612245) equal to 1.6344378 and -1.6344378.

Subproblem 1
x + -0.6530612245 = 1.6344378

Simplifying
x + -0.6530612245 = 1.6344378

Reorder the terms:
-0.6530612245 + x = 1.6344378

Solving
-0.6530612245 + x = 1.6344378

Solving for variable 'x'.

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

Add '0.6530612245' to each side of the equation.
-0.6530612245 + 0.6530612245 + x = 1.6344378 + 0.6530612245

Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000
0.0000000000 + x = 1.6344378 + 0.6530612245
x = 1.6344378 + 0.6530612245

Combine like terms: 1.6344378 + 0.6530612245 = 2.2874990245
x = 2.2874990245

Simplifying
x = 2.2874990245

Subproblem 2
x + -0.6530612245 = -1.6344378

Simplifying
x + -0.6530612245 = -1.6344378

Reorder the terms:
-0.6530612245 + x = -1.6344378

Solving
-0.6530612245 + x = -1.6344378

Solving for variable 'x'.

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

Add '0.6530612245' to each side of the equation.
-0.6530612245 + 0.6530612245 + x = -1.6344378 + 0.6530612245

Combine like terms: -0.6530612245 + 0.6530612245 = 0.0000000000
0.0000000000 + x = -1.6344378 + 0.6530612245
x = -1.6344378 + 0.6530612245

Combine like terms: -1.6344378 + 0.6530612245 = -0.9813765755
x = -0.9813765755

Simplifying
x = -0.9813765755

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2874990245, -0.9813765755}