x^2-4.7x-28=0

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Solution for x^2-4.7x-28=0 equation: 


Simplifying
x2 + -4.7x + -28 = 0

Reorder the terms:
-28 + -4.7x + x2 = 0

Solving
-28 + -4.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -4.7x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + -4.7x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -4.7x + x2 = 0 + 28
-4.7x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
-4.7x + x2 = 28

The x term is -4.7x.  Take half its coefficient (-2.35).
Square it (5.5225) and add it to both sides.

Add '5.5225' to each side of the equation.
-4.7x + 5.5225 + x2 = 28 + 5.5225

Reorder the terms:
5.5225 + -4.7x + x2 = 28 + 5.5225

Combine like terms: 28 + 5.5225 = 33.5225
5.5225 + -4.7x + x2 = 33.5225

Factor a perfect square on the left side:
(x + -2.35)(x + -2.35) = 33.5225

Calculate the square root of the right side: 5.789861829

Break this problem into two subproblems by setting 
(x + -2.35) equal to 5.789861829 and -5.789861829.


Subproblem 1
x + -2.35 = 5.789861829

Simplifying
x + -2.35 = 5.789861829

Reorder the terms:
-2.35 + x = 5.789861829

Solving
-2.35 + x = 5.789861829

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = 5.789861829 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = 5.789861829 + 2.35
x = 5.789861829 + 2.35

Combine like terms: 5.789861829 + 2.35 = 8.139861829
x = 8.139861829

Simplifying
x = 8.139861829


Subproblem 2
x + -2.35 = -5.789861829

Simplifying
x + -2.35 = -5.789861829

Reorder the terms:
-2.35 + x = -5.789861829

Solving
-2.35 + x = -5.789861829

Solving for variable 'x'.

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

Add '2.35' to each side of the equation.
-2.35 + 2.35 + x = -5.789861829 + 2.35

Combine like terms: -2.35 + 2.35 = 0.00
0.00 + x = -5.789861829 + 2.35
x = -5.789861829 + 2.35

Combine like terms: -5.789861829 + 2.35 = -3.439861829
x = -3.439861829

Simplifying
x = -3.439861829


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.139861829, -3.439861829}

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