x^2+4.7x=-2.8

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Solution for x^2+4.7x=-2.8 equation: 


Simplifying
x2 + 4.7x = -2.8

Reorder the terms:
4.7x + x2 = -2.8

Solving
4.7x + x2 = -2.8

Solving for variable 'x'.

Reorder the terms:
2.8 + 4.7x + x2 = -2.8 + 2.8

Combine like terms: -2.8 + 2.8 = 0.0
2.8 + 4.7x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + 4.7x + -2.8 + x2 = 0.0 + -2.8

Reorder the terms:
2.8 + -2.8 + 4.7x + x2 = 0.0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + 4.7x + x2 = 0.0 + -2.8
4.7x + x2 = 0.0 + -2.8

Combine like terms: 0.0 + -2.8 = -2.8
4.7x + x2 = -2.8

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 = -2.8 + 5.5225

Reorder the terms:
5.5225 + 4.7x + x2 = -2.8 + 5.5225

Combine like terms: -2.8 + 5.5225 = 2.7225
5.5225 + 4.7x + x2 = 2.7225

Factor a perfect square on the left side:
(x + 2.35)(x + 2.35) = 2.7225

Calculate the square root of the right side: 1.65

Break this problem into two subproblems by setting 
(x + 2.35) equal to 1.65 and -1.65.


Subproblem 1
x + 2.35 = 1.65

Simplifying
x + 2.35 = 1.65

Reorder the terms:
2.35 + x = 1.65

Solving
2.35 + x = 1.65

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 = 1.65 + -2.35

Combine like terms: 2.35 + -2.35 = 0.00
0.00 + x = 1.65 + -2.35
x = 1.65 + -2.35

Combine like terms: 1.65 + -2.35 = -0.7
x = -0.7

Simplifying
x = -0.7


Subproblem 2
x + 2.35 = -1.65

Simplifying
x + 2.35 = -1.65

Reorder the terms:
2.35 + x = -1.65

Solving
2.35 + x = -1.65

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 = -1.65 + -2.35

Combine like terms: 2.35 + -2.35 = 0.00
0.00 + x = -1.65 + -2.35
x = -1.65 + -2.35

Combine like terms: -1.65 + -2.35 = -4
x = -4

Simplifying
x = -4


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.7, -4}

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