0=.3x^2+2.43x+4.902

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Solution for 0=.3x^2+2.43x+4.902 equation: 


Simplifying
0 = 0.3x2 + 2.43x + 4.902

Reorder the terms:
0 = 4.902 + 2.43x + 0.3x2

Solving
0 = 4.902 + 2.43x + 0.3x2

Solving for variable 'x'.

Combine like terms: 0 + -4.902 = -4.902
-4.902 + -2.43x + -0.3x2 = 4.902 + 2.43x + 0.3x2 + -4.902 + -2.43x + -0.3x2

Reorder the terms:
-4.902 + -2.43x + -0.3x2 = 4.902 + -4.902 + 2.43x + -2.43x + 0.3x2 + -0.3x2

Combine like terms: 4.902 + -4.902 = 0.000
-4.902 + -2.43x + -0.3x2 = 0.000 + 2.43x + -2.43x + 0.3x2 + -0.3x2
-4.902 + -2.43x + -0.3x2 = 2.43x + -2.43x + 0.3x2 + -0.3x2

Combine like terms: 2.43x + -2.43x = 0.00
-4.902 + -2.43x + -0.3x2 = 0.00 + 0.3x2 + -0.3x2
-4.902 + -2.43x + -0.3x2 = 0.3x2 + -0.3x2

Combine like terms: 0.3x2 + -0.3x2 = 0.0
-4.902 + -2.43x + -0.3x2 = 0.0

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
16.34 + 8.1x + x2 = 0

Move the constant term to the right:

Add '-16.34' to each side of the equation.
16.34 + 8.1x + -16.34 + x2 = 0 + -16.34

Reorder the terms:
16.34 + -16.34 + 8.1x + x2 = 0 + -16.34

Combine like terms: 16.34 + -16.34 = 0.00
0.00 + 8.1x + x2 = 0 + -16.34
8.1x + x2 = 0 + -16.34

Combine like terms: 0 + -16.34 = -16.34
8.1x + x2 = -16.34

The x term is 8.1x.  Take half its coefficient (4.05).
Square it (16.4025) and add it to both sides.

Add '16.4025' to each side of the equation.
8.1x + 16.4025 + x2 = -16.34 + 16.4025

Reorder the terms:
16.4025 + 8.1x + x2 = -16.34 + 16.4025

Combine like terms: -16.34 + 16.4025 = 0.0625
16.4025 + 8.1x + x2 = 0.0625

Factor a perfect square on the left side:
(x + 4.05)(x + 4.05) = 0.0625

Calculate the square root of the right side: 0.25

Break this problem into two subproblems by setting 
(x + 4.05) equal to 0.25 and -0.25.


Subproblem 1
x + 4.05 = 0.25

Simplifying
x + 4.05 = 0.25

Reorder the terms:
4.05 + x = 0.25

Solving
4.05 + x = 0.25

Solving for variable 'x'.

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

Add '-4.05' to each side of the equation.
4.05 + -4.05 + x = 0.25 + -4.05

Combine like terms: 4.05 + -4.05 = 0.00
0.00 + x = 0.25 + -4.05
x = 0.25 + -4.05

Combine like terms: 0.25 + -4.05 = -3.8
x = -3.8

Simplifying
x = -3.8


Subproblem 2
x + 4.05 = -0.25

Simplifying
x + 4.05 = -0.25

Reorder the terms:
4.05 + x = -0.25

Solving
4.05 + x = -0.25

Solving for variable 'x'.

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

Add '-4.05' to each side of the equation.
4.05 + -4.05 + x = -0.25 + -4.05

Combine like terms: 4.05 + -4.05 = 0.00
0.00 + x = -0.25 + -4.05
x = -0.25 + -4.05

Combine like terms: -0.25 + -4.05 = -4.3
x = -4.3

Simplifying
x = -4.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.8, -4.3}

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