x^2+2.8x-5=0

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Solution for x^2+2.8x-5=0 equation: 


Simplifying
x2 + 2.8x + -5 = 0

Reorder the terms:
-5 + 2.8x + x2 = 0

Solving
-5 + 2.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2.8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 2.8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2.8x + x2 = 0 + 5
2.8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
2.8x + x2 = 5

The x term is 2.8x.  Take half its coefficient (1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
2.8x + 1.96 + x2 = 5 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 5 + 1.96

Combine like terms: 5 + 1.96 = 6.96
1.96 + 2.8x + x2 = 6.96

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 6.96

Calculate the square root of the right side: 2.638181192

Break this problem into two subproblems by setting 
(x + 1.4) equal to 2.638181192 and -2.638181192.


Subproblem 1
x + 1.4 = 2.638181192

Simplifying
x + 1.4 = 2.638181192

Reorder the terms:
1.4 + x = 2.638181192

Solving
1.4 + x = 2.638181192

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = 2.638181192 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = 2.638181192 + -1.4
x = 2.638181192 + -1.4

Combine like terms: 2.638181192 + -1.4 = 1.238181192
x = 1.238181192

Simplifying
x = 1.238181192


Subproblem 2
x + 1.4 = -2.638181192

Simplifying
x + 1.4 = -2.638181192

Reorder the terms:
1.4 + x = -2.638181192

Solving
1.4 + x = -2.638181192

Solving for variable 'x'.

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

Add '-1.4' to each side of the equation.
1.4 + -1.4 + x = -2.638181192 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = -2.638181192 + -1.4
x = -2.638181192 + -1.4

Combine like terms: -2.638181192 + -1.4 = -4.038181192
x = -4.038181192

Simplifying
x = -4.038181192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.238181192, -4.038181192}

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