490x^2+71x-113=0

Solution for 490x^2+71x-113=0 equation:

Simplifying
490x2 + 71x + -113 = 0

Reorder the terms:
-113 + 71x + 490x2 = 0

Solving
-113 + 71x + 490x2 = 0

Solving for variable 'x'.

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

Divide each side by '490'.
-0.2306122449 + 0.1448979592x + x2 = 0

Move the constant term to the right:

Add '0.2306122449' to each side of the equation.
-0.2306122449 + 0.1448979592x + 0.2306122449 + x2 = 0 + 0.2306122449

Reorder the terms:
-0.2306122449 + 0.2306122449 + 0.1448979592x + x2 = 0 + 0.2306122449

Combine like terms: -0.2306122449 + 0.2306122449 = 0.0000000000
0.0000000000 + 0.1448979592x + x2 = 0 + 0.2306122449
0.1448979592x + x2 = 0 + 0.2306122449

Combine like terms: 0 + 0.2306122449 = 0.2306122449
0.1448979592x + x2 = 0.2306122449

The x term is 0.1448979592x.  Take half its coefficient (0.0724489796).
Square it (0.005248854645) and add it to both sides.

Add '0.005248854645' to each side of the equation.
0.1448979592x + 0.005248854645 + x2 = 0.2306122449 + 0.005248854645

Reorder the terms:
0.005248854645 + 0.1448979592x + x2 = 0.2306122449 + 0.005248854645

Combine like terms: 0.2306122449 + 0.005248854645 = 0.235861099545
0.005248854645 + 0.1448979592x + x2 = 0.235861099545

Factor a perfect square on the left side:
(x + 0.0724489796)(x + 0.0724489796) = 0.235861099545

Calculate the square root of the right side: 0.48565533

Break this problem into two subproblems by setting 
(x + 0.0724489796) equal to 0.48565533 and -0.48565533.

Subproblem 1
x + 0.0724489796 = 0.48565533

Simplifying
x + 0.0724489796 = 0.48565533

Reorder the terms:
0.0724489796 + x = 0.48565533

Solving
0.0724489796 + x = 0.48565533

Solving for variable 'x'.

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

Add '-0.0724489796' to each side of the equation.
0.0724489796 + -0.0724489796 + x = 0.48565533 + -0.0724489796

Combine like terms: 0.0724489796 + -0.0724489796 = 0.0000000000
0.0000000000 + x = 0.48565533 + -0.0724489796
x = 0.48565533 + -0.0724489796

Combine like terms: 0.48565533 + -0.0724489796 = 0.4132063504
x = 0.4132063504

Simplifying
x = 0.4132063504

Subproblem 2
x + 0.0724489796 = -0.48565533

Simplifying
x + 0.0724489796 = -0.48565533

Reorder the terms:
0.0724489796 + x = -0.48565533

Solving
0.0724489796 + x = -0.48565533

Solving for variable 'x'.

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

Add '-0.0724489796' to each side of the equation.
0.0724489796 + -0.0724489796 + x = -0.48565533 + -0.0724489796

Combine like terms: 0.0724489796 + -0.0724489796 = 0.0000000000
0.0000000000 + x = -0.48565533 + -0.0724489796
x = -0.48565533 + -0.0724489796

Combine like terms: -0.48565533 + -0.0724489796 = -0.5581043096
x = -0.5581043096

Simplifying
x = -0.5581043096

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4132063504, -0.5581043096}