x^2+2.86x-21428.57=0

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Solution for x^2+2.86x-21428.57=0 equation: 


Simplifying
x2 + 2.86x + -21428.57 = 0

Reorder the terms:
-21428.57 + 2.86x + x2 = 0

Solving
-21428.57 + 2.86x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '21428.57' to each side of the equation.
-21428.57 + 2.86x + 21428.57 + x2 = 0 + 21428.57

Reorder the terms:
-21428.57 + 21428.57 + 2.86x + x2 = 0 + 21428.57

Combine like terms: -21428.57 + 21428.57 = 0.00
0.00 + 2.86x + x2 = 0 + 21428.57
2.86x + x2 = 0 + 21428.57

Combine like terms: 0 + 21428.57 = 21428.57
2.86x + x2 = 21428.57

The x term is 2.86x.  Take half its coefficient (1.43).
Square it (2.0449) and add it to both sides.

Add '2.0449' to each side of the equation.
2.86x + 2.0449 + x2 = 21428.57 + 2.0449

Reorder the terms:
2.0449 + 2.86x + x2 = 21428.57 + 2.0449

Combine like terms: 21428.57 + 2.0449 = 21430.6149
2.0449 + 2.86x + x2 = 21430.6149

Factor a perfect square on the left side:
(x + 1.43)(x + 1.43) = 21430.6149

Calculate the square root of the right side: 146.39199056

Break this problem into two subproblems by setting 
(x + 1.43) equal to 146.39199056 and -146.39199056.


Subproblem 1
x + 1.43 = 146.39199056

Simplifying
x + 1.43 = 146.39199056

Reorder the terms:
1.43 + x = 146.39199056

Solving
1.43 + x = 146.39199056

Solving for variable 'x'.

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

Add '-1.43' to each side of the equation.
1.43 + -1.43 + x = 146.39199056 + -1.43

Combine like terms: 1.43 + -1.43 = 0.00
0.00 + x = 146.39199056 + -1.43
x = 146.39199056 + -1.43

Combine like terms: 146.39199056 + -1.43 = 144.96199056
x = 144.96199056

Simplifying
x = 144.96199056


Subproblem 2
x + 1.43 = -146.39199056

Simplifying
x + 1.43 = -146.39199056

Reorder the terms:
1.43 + x = -146.39199056

Solving
1.43 + x = -146.39199056

Solving for variable 'x'.

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

Add '-1.43' to each side of the equation.
1.43 + -1.43 + x = -146.39199056 + -1.43

Combine like terms: 1.43 + -1.43 = 0.00
0.00 + x = -146.39199056 + -1.43
x = -146.39199056 + -1.43

Combine like terms: -146.39199056 + -1.43 = -147.82199056
x = -147.82199056

Simplifying
x = -147.82199056


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {144.96199056, -147.82199056}

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