x^2+2.8x-1.96=6.69

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Solution for x^2+2.8x-1.96=6.69 equation: 


Simplifying
x2 + 2.8x + -1.96 = 6.69

Reorder the terms:
-1.96 + 2.8x + x2 = 6.69

Solving
-1.96 + 2.8x + x2 = 6.69

Solving for variable 'x'.

Reorder the terms:
-1.96 + -6.69 + 2.8x + x2 = 6.69 + -6.69

Combine like terms: -1.96 + -6.69 = -8.65
-8.65 + 2.8x + x2 = 6.69 + -6.69

Combine like terms: 6.69 + -6.69 = 0.00
-8.65 + 2.8x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '8.65' to each side of the equation.
-8.65 + 2.8x + 8.65 + x2 = 0.00 + 8.65

Reorder the terms:
-8.65 + 8.65 + 2.8x + x2 = 0.00 + 8.65

Combine like terms: -8.65 + 8.65 = 0.00
0.00 + 2.8x + x2 = 0.00 + 8.65
2.8x + x2 = 0.00 + 8.65

Combine like terms: 0.00 + 8.65 = 8.65
2.8x + x2 = 8.65

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 = 8.65 + 1.96

Reorder the terms:
1.96 + 2.8x + x2 = 8.65 + 1.96

Combine like terms: 8.65 + 1.96 = 10.61
1.96 + 2.8x + x2 = 10.61

Factor a perfect square on the left side:
(x + 1.4)(x + 1.4) = 10.61

Calculate the square root of the right side: 3.257299495

Break this problem into two subproblems by setting 
(x + 1.4) equal to 3.257299495 and -3.257299495.


Subproblem 1
x + 1.4 = 3.257299495

Simplifying
x + 1.4 = 3.257299495

Reorder the terms:
1.4 + x = 3.257299495

Solving
1.4 + x = 3.257299495

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 = 3.257299495 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = 3.257299495 + -1.4
x = 3.257299495 + -1.4

Combine like terms: 3.257299495 + -1.4 = 1.857299495
x = 1.857299495

Simplifying
x = 1.857299495


Subproblem 2
x + 1.4 = -3.257299495

Simplifying
x + 1.4 = -3.257299495

Reorder the terms:
1.4 + x = -3.257299495

Solving
1.4 + x = -3.257299495

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 = -3.257299495 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + x = -3.257299495 + -1.4
x = -3.257299495 + -1.4

Combine like terms: -3.257299495 + -1.4 = -4.657299495
x = -4.657299495

Simplifying
x = -4.657299495


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.857299495, -4.657299495}

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