2x^2+28x+47=-7

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Solution for 2x^2+28x+47=-7 equation: 


Simplifying
2x2 + 28x + 47 = -7

Reorder the terms:
47 + 28x + 2x2 = -7

Solving
47 + 28x + 2x2 = -7

Solving for variable 'x'.

Reorder the terms:
47 + 7 + 28x + 2x2 = -7 + 7

Combine like terms: 47 + 7 = 54
54 + 28x + 2x2 = -7 + 7

Combine like terms: -7 + 7 = 0
54 + 28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(27 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
27 + 14x + x2 = 0

Solving
27 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 14x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + 14x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 14x + x2 = 0 + -27
14x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
14x + x2 = -27

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -27 + 49

Reorder the terms:
49 + 14x + x2 = -27 + 49

Combine like terms: -27 + 49 = 22
49 + 14x + x2 = 22

Factor a perfect square on the left side:
(x + 7)(x + 7) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(x + 7) equal to 4.69041576 and -4.69041576.


Subproblem 1
x + 7 = 4.69041576

Simplifying
x + 7 = 4.69041576

Reorder the terms:
7 + x = 4.69041576

Solving
7 + x = 4.69041576

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 4.69041576 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.69041576 + -7
x = 4.69041576 + -7

Combine like terms: 4.69041576 + -7 = -2.30958424
x = -2.30958424

Simplifying
x = -2.30958424


Subproblem 2
x + 7 = -4.69041576

Simplifying
x + 7 = -4.69041576

Reorder the terms:
7 + x = -4.69041576

Solving
7 + x = -4.69041576

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -4.69041576 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.69041576 + -7
x = -4.69041576 + -7

Combine like terms: -4.69041576 + -7 = -11.69041576
x = -11.69041576

Simplifying
x = -11.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.30958424, -11.69041576}
Solution
x = {-2.30958424, -11.69041576}

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