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 = 8.3225
5.5225 + 4.7x + x2 = 8.3225

Factor a perfect square on the left side:
(x + 2.35)(x + 2.35) = 8.3225

Calculate the square root of the right side: 2.884874347

Break this problem into two subproblems by setting 
(x + 2.35) equal to 2.884874347 and -2.884874347.


Subproblem 1
x + 2.35 = 2.884874347

Simplifying
x + 2.35 = 2.884874347

Reorder the terms:
2.35 + x = 2.884874347

Solving
2.35 + x = 2.884874347

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 = 2.884874347 + -2.35

Combine like terms: 2.35 + -2.35 = 0.00
0.00 + x = 2.884874347 + -2.35
x = 2.884874347 + -2.35

Combine like terms: 2.884874347 + -2.35 = 0.534874347
x = 0.534874347

Simplifying
x = 0.534874347


Subproblem 2
x + 2.35 = -2.884874347

Simplifying
x + 2.35 = -2.884874347

Reorder the terms:
2.35 + x = -2.884874347

Solving
2.35 + x = -2.884874347

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 = -2.884874347 + -2.35

Combine like terms: 2.35 + -2.35 = 0.00
0.00 + x = -2.884874347 + -2.35
x = -2.884874347 + -2.35

Combine like terms: -2.884874347 + -2.35 = -5.234874347
x = -5.234874347

Simplifying
x = -5.234874347


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.534874347, -5.234874347}

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