x^2+0.714x-0.153=0

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Solution for x^2+0.714x-0.153=0 equation: 


Simplifying
x2 + 0.714x + -0.153 = 0

Reorder the terms:
-0.153 + 0.714x + x2 = 0

Solving
-0.153 + 0.714x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.153' to each side of the equation.
-0.153 + 0.714x + 0.153 + x2 = 0 + 0.153

Reorder the terms:
-0.153 + 0.153 + 0.714x + x2 = 0 + 0.153

Combine like terms: -0.153 + 0.153 = 0.000
0.000 + 0.714x + x2 = 0 + 0.153
0.714x + x2 = 0 + 0.153

Combine like terms: 0 + 0.153 = 0.153
0.714x + x2 = 0.153

The x term is 0.714x.  Take half its coefficient (0.357).
Square it (0.127449) and add it to both sides.

Add '0.127449' to each side of the equation.
0.714x + 0.127449 + x2 = 0.153 + 0.127449

Reorder the terms:
0.127449 + 0.714x + x2 = 0.153 + 0.127449

Combine like terms: 0.153 + 0.127449 = 0.280449
0.127449 + 0.714x + x2 = 0.280449

Factor a perfect square on the left side:
(x + 0.357)(x + 0.357) = 0.280449

Calculate the square root of the right side: 0.529574357

Break this problem into two subproblems by setting 
(x + 0.357) equal to 0.529574357 and -0.529574357.


Subproblem 1
x + 0.357 = 0.529574357

Simplifying
x + 0.357 = 0.529574357

Reorder the terms:
0.357 + x = 0.529574357

Solving
0.357 + x = 0.529574357

Solving for variable 'x'.

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

Add '-0.357' to each side of the equation.
0.357 + -0.357 + x = 0.529574357 + -0.357

Combine like terms: 0.357 + -0.357 = 0.000
0.000 + x = 0.529574357 + -0.357
x = 0.529574357 + -0.357

Combine like terms: 0.529574357 + -0.357 = 0.172574357
x = 0.172574357

Simplifying
x = 0.172574357


Subproblem 2
x + 0.357 = -0.529574357

Simplifying
x + 0.357 = -0.529574357

Reorder the terms:
0.357 + x = -0.529574357

Solving
0.357 + x = -0.529574357

Solving for variable 'x'.

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

Add '-0.357' to each side of the equation.
0.357 + -0.357 + x = -0.529574357 + -0.357

Combine like terms: 0.357 + -0.357 = 0.000
0.000 + x = -0.529574357 + -0.357
x = -0.529574357 + -0.357

Combine like terms: -0.529574357 + -0.357 = -0.886574357
x = -0.886574357

Simplifying
x = -0.886574357


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.172574357, -0.886574357}

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