-3x^2-0.14x+0.49=0

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Solution for -3x^2-0.14x+0.49=0 equation:


Simplifying
-3x2 + -0.14x + 0.49 = 0

Reorder the terms:
0.49 + -0.14x + -3x2 = 0

Solving
0.49 + -0.14x + -3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-0.1633333333 + 0.04666666667x + x2 = 0

Move the constant term to the right:

Add '0.1633333333' to each side of the equation.
-0.1633333333 + 0.04666666667x + 0.1633333333 + x2 = 0 + 0.1633333333

Reorder the terms:
-0.1633333333 + 0.1633333333 + 0.04666666667x + x2 = 0 + 0.1633333333

Combine like terms: -0.1633333333 + 0.1633333333 = 0.0000000000
0.0000000000 + 0.04666666667x + x2 = 0 + 0.1633333333
0.04666666667x + x2 = 0 + 0.1633333333

Combine like terms: 0 + 0.1633333333 = 0.1633333333
0.04666666667x + x2 = 0.1633333333

The x term is 0.04666666667x.  Take half its coefficient (0.02333333334).
Square it (0.0005444444448) and add it to both sides.

Add '0.0005444444448' to each side of the equation.
0.04666666667x + 0.0005444444448 + x2 = 0.1633333333 + 0.0005444444448

Reorder the terms:
0.0005444444448 + 0.04666666667x + x2 = 0.1633333333 + 0.0005444444448

Combine like terms: 0.1633333333 + 0.0005444444448 = 0.1638777777448
0.0005444444448 + 0.04666666667x + x2 = 0.1638777777448

Factor a perfect square on the left side:
(x + 0.02333333334)(x + 0.02333333334) = 0.1638777777448

Calculate the square root of the right side: 0.404818203

Break this problem into two subproblems by setting 
(x + 0.02333333334) equal to 0.404818203 and -0.404818203.


Subproblem 1
x + 0.02333333334 = 0.404818203

Simplifying
x + 0.02333333334 = 0.404818203

Reorder the terms:
0.02333333334 + x = 0.404818203

Solving
0.02333333334 + x = 0.404818203

Solving for variable 'x'.

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

Add '-0.02333333334' to each side of the equation.
0.02333333334 + -0.02333333334 + x = 0.404818203 + -0.02333333334

Combine like terms: 0.02333333334 + -0.02333333334 = 0.00000000000
0.00000000000 + x = 0.404818203 + -0.02333333334
x = 0.404818203 + -0.02333333334

Combine like terms: 0.404818203 + -0.02333333334 = 0.38148486966
x = 0.38148486966

Simplifying
x = 0.38148486966


Subproblem 2
x + 0.02333333334 = -0.404818203

Simplifying
x + 0.02333333334 = -0.404818203

Reorder the terms:
0.02333333334 + x = -0.404818203

Solving
0.02333333334 + x = -0.404818203

Solving for variable 'x'.

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

Add '-0.02333333334' to each side of the equation.
0.02333333334 + -0.02333333334 + x = -0.404818203 + -0.02333333334

Combine like terms: 0.02333333334 + -0.02333333334 = 0.00000000000
0.00000000000 + x = -0.404818203 + -0.02333333334
x = -0.404818203 + -0.02333333334

Combine like terms: -0.404818203 + -0.02333333334 = -0.42815153634
x = -0.42815153634

Simplifying
x = -0.42815153634


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.38148486966, -0.42815153634}

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