5x^2+27x+14=0

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Solution for 5x^2+27x+14=0 equation: 


Simplifying
5x2 + 27x + 14 = 0

Reorder the terms:
14 + 27x + 5x2 = 0

Solving
14 + 27x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.8 + 5.4x + x2 = 0

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + 5.4x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + 5.4x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + 5.4x + x2 = 0 + -2.8
5.4x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
5.4x + x2 = -2.8

The x term is 5.4x.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4x + 7.29 + x2 = -2.8 + 7.29

Reorder the terms:
7.29 + 5.4x + x2 = -2.8 + 7.29

Combine like terms: -2.8 + 7.29 = 4.49
7.29 + 5.4x + x2 = 4.49

Factor a perfect square on the left side:
(x + 2.7)(x + 2.7) = 4.49

Calculate the square root of the right side: 2.11896201

Break this problem into two subproblems by setting 
(x + 2.7) equal to 2.11896201 and -2.11896201.


Subproblem 1
x + 2.7 = 2.11896201

Simplifying
x + 2.7 = 2.11896201

Reorder the terms:
2.7 + x = 2.11896201

Solving
2.7 + x = 2.11896201

Solving for variable 'x'.

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

Add '-2.7' to each side of the equation.
2.7 + -2.7 + x = 2.11896201 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + x = 2.11896201 + -2.7
x = 2.11896201 + -2.7

Combine like terms: 2.11896201 + -2.7 = -0.58103799
x = -0.58103799

Simplifying
x = -0.58103799


Subproblem 2
x + 2.7 = -2.11896201

Simplifying
x + 2.7 = -2.11896201

Reorder the terms:
2.7 + x = -2.11896201

Solving
2.7 + x = -2.11896201

Solving for variable 'x'.

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

Add '-2.7' to each side of the equation.
2.7 + -2.7 + x = -2.11896201 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + x = -2.11896201 + -2.7
x = -2.11896201 + -2.7

Combine like terms: -2.11896201 + -2.7 = -4.81896201
x = -4.81896201

Simplifying
x = -4.81896201


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.58103799, -4.81896201}

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