4.9x^2+5x-250=0

Solution for 4.9x^2+5x-250=0 equation:

Simplifying
4.9x2 + 5x + -250 = 0

Reorder the terms:
-250 + 5x + 4.9x2 = 0

Solving
-250 + 5x + 4.9x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.9'.
-51.02040816 + 1.020408163x + x2 = 0

Move the constant term to the right:

Add '51.02040816' to each side of the equation.
-51.02040816 + 1.020408163x + 51.02040816 + x2 = 0 + 51.02040816

Reorder the terms:
-51.02040816 + 51.02040816 + 1.020408163x + x2 = 0 + 51.02040816

Combine like terms: -51.02040816 + 51.02040816 = 0.00000000
0.00000000 + 1.020408163x + x2 = 0 + 51.02040816
1.020408163x + x2 = 0 + 51.02040816

Combine like terms: 0 + 51.02040816 = 51.02040816
1.020408163x + x2 = 51.02040816

The x term is 1.020408163x.  Take half its coefficient (0.5102040815).
Square it (0.2603082048) and add it to both sides.

Add '0.2603082048' to each side of the equation.
1.020408163x + 0.2603082048 + x2 = 51.02040816 + 0.2603082048

Reorder the terms:
0.2603082048 + 1.020408163x + x2 = 51.02040816 + 0.2603082048

Combine like terms: 51.02040816 + 0.2603082048 = 51.2807163648
0.2603082048 + 1.020408163x + x2 = 51.2807163648

Factor a perfect square on the left side:
(x + 0.5102040815)(x + 0.5102040815) = 51.2807163648

Calculate the square root of the right side: 7.161055534

Break this problem into two subproblems by setting 
(x + 0.5102040815) equal to 7.161055534 and -7.161055534.

Subproblem 1
x + 0.5102040815 = 7.161055534

Simplifying
x + 0.5102040815 = 7.161055534

Reorder the terms:
0.5102040815 + x = 7.161055534

Solving
0.5102040815 + x = 7.161055534

Solving for variable 'x'.

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

Add '-0.5102040815' to each side of the equation.
0.5102040815 + -0.5102040815 + x = 7.161055534 + -0.5102040815

Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000
0.0000000000 + x = 7.161055534 + -0.5102040815
x = 7.161055534 + -0.5102040815

Combine like terms: 7.161055534 + -0.5102040815 = 6.6508514525
x = 6.6508514525

Simplifying
x = 6.6508514525

Subproblem 2
x + 0.5102040815 = -7.161055534

Simplifying
x + 0.5102040815 = -7.161055534

Reorder the terms:
0.5102040815 + x = -7.161055534

Solving
0.5102040815 + x = -7.161055534

Solving for variable 'x'.

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

Add '-0.5102040815' to each side of the equation.
0.5102040815 + -0.5102040815 + x = -7.161055534 + -0.5102040815

Combine like terms: 0.5102040815 + -0.5102040815 = 0.0000000000
0.0000000000 + x = -7.161055534 + -0.5102040815
x = -7.161055534 + -0.5102040815

Combine like terms: -7.161055534 + -0.5102040815 = -7.6712596155
x = -7.6712596155

Simplifying
x = -7.6712596155

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.6508514525, -7.6712596155}