x^2+.49x-30.25=0

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Solution for x^2+.49x-30.25=0 equation: 


Simplifying
x2 + 0.49x + -30.25 = 0

Reorder the terms:
-30.25 + 0.49x + x2 = 0

Solving
-30.25 + 0.49x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '30.25' to each side of the equation.
-30.25 + 0.49x + 30.25 + x2 = 0 + 30.25

Reorder the terms:
-30.25 + 30.25 + 0.49x + x2 = 0 + 30.25

Combine like terms: -30.25 + 30.25 = 0.00
0.00 + 0.49x + x2 = 0 + 30.25
0.49x + x2 = 0 + 30.25

Combine like terms: 0 + 30.25 = 30.25
0.49x + x2 = 30.25

The x term is 0.49x.  Take half its coefficient (0.245).
Square it (0.060025) and add it to both sides.

Add '0.060025' to each side of the equation.
0.49x + 0.060025 + x2 = 30.25 + 0.060025

Reorder the terms:
0.060025 + 0.49x + x2 = 30.25 + 0.060025

Combine like terms: 30.25 + 0.060025 = 30.310025
0.060025 + 0.49x + x2 = 30.310025

Factor a perfect square on the left side:
(x + 0.245)(x + 0.245) = 30.310025

Calculate the square root of the right side: 5.505454114

Break this problem into two subproblems by setting 
(x + 0.245) equal to 5.505454114 and -5.505454114.


Subproblem 1
x + 0.245 = 5.505454114

Simplifying
x + 0.245 = 5.505454114

Reorder the terms:
0.245 + x = 5.505454114

Solving
0.245 + x = 5.505454114

Solving for variable 'x'.

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

Add '-0.245' to each side of the equation.
0.245 + -0.245 + x = 5.505454114 + -0.245

Combine like terms: 0.245 + -0.245 = 0.000
0.000 + x = 5.505454114 + -0.245
x = 5.505454114 + -0.245

Combine like terms: 5.505454114 + -0.245 = 5.260454114
x = 5.260454114

Simplifying
x = 5.260454114


Subproblem 2
x + 0.245 = -5.505454114

Simplifying
x + 0.245 = -5.505454114

Reorder the terms:
0.245 + x = -5.505454114

Solving
0.245 + x = -5.505454114

Solving for variable 'x'.

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

Add '-0.245' to each side of the equation.
0.245 + -0.245 + x = -5.505454114 + -0.245

Combine like terms: 0.245 + -0.245 = 0.000
0.000 + x = -5.505454114 + -0.245
x = -5.505454114 + -0.245

Combine like terms: -5.505454114 + -0.245 = -5.750454114
x = -5.750454114

Simplifying
x = -5.750454114


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.260454114, -5.750454114}

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