x^2-2.8x-47.04=0

Solution for x^2-2.8x-47.04=0 equation:

Simplifying
x2 + -2.8x + -47.04 = 0

Reorder the terms:
-47.04 + -2.8x + x2 = 0

Solving
-47.04 + -2.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '47.04' to each side of the equation.
-47.04 + -2.8x + 47.04 + x2 = 0 + 47.04

Reorder the terms:
-47.04 + 47.04 + -2.8x + x2 = 0 + 47.04

Combine like terms: -47.04 + 47.04 = 0.00
0.00 + -2.8x + x2 = 0 + 47.04
-2.8x + x2 = 0 + 47.04

Combine like terms: 0 + 47.04 = 47.04
-2.8x + x2 = 47.04

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 = 47.04 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = 47.04 + 1.96

Combine like terms: 47.04 + 1.96 = 49
1.96 + -2.8x + x2 = 49

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 49

Calculate the square root of the right side: 7

Break this problem into two subproblems by setting 
(x + -1.4) equal to 7 and -7.

Subproblem 1
x + -1.4 = 7

Simplifying
x + -1.4 = 7

Reorder the terms:
-1.4 + x = 7

Solving
-1.4 + x = 7

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 = 7 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 7 + 1.4
x = 7 + 1.4

Combine like terms: 7 + 1.4 = 8.4
x = 8.4

Simplifying
x = 8.4

Subproblem 2
x + -1.4 = -7

Simplifying
x + -1.4 = -7

Reorder the terms:
-1.4 + x = -7

Solving
-1.4 + x = -7

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 = -7 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -7 + 1.4
x = -7 + 1.4

Combine like terms: -7 + 1.4 = -5.6
x = -5.6

Simplifying
x = -5.6

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.4, -5.6}