2x^2+29x+5.3=0

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Solution for 2x^2+29x+5.3=0 equation: 


Simplifying
2x2 + 29x + 5.3 = 0

Reorder the terms:
5.3 + 29x + 2x2 = 0

Solving
5.3 + 29x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
2.65 + 14.5x + x2 = 0

Move the constant term to the right:

Add '-2.65' to each side of the equation.
2.65 + 14.5x + -2.65 + x2 = 0 + -2.65

Reorder the terms:
2.65 + -2.65 + 14.5x + x2 = 0 + -2.65

Combine like terms: 2.65 + -2.65 = 0.00
0.00 + 14.5x + x2 = 0 + -2.65
14.5x + x2 = 0 + -2.65

Combine like terms: 0 + -2.65 = -2.65
14.5x + x2 = -2.65

The x term is 14.5x.  Take half its coefficient (7.25).
Square it (52.5625) and add it to both sides.

Add '52.5625' to each side of the equation.
14.5x + 52.5625 + x2 = -2.65 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = -2.65 + 52.5625

Combine like terms: -2.65 + 52.5625 = 49.9125
52.5625 + 14.5x + x2 = 49.9125

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 49.9125

Calculate the square root of the right side: 7.064877918

Break this problem into two subproblems by setting 
(x + 7.25) equal to 7.064877918 and -7.064877918.


Subproblem 1
x + 7.25 = 7.064877918

Simplifying
x + 7.25 = 7.064877918

Reorder the terms:
7.25 + x = 7.064877918

Solving
7.25 + x = 7.064877918

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = 7.064877918 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 7.064877918 + -7.25
x = 7.064877918 + -7.25

Combine like terms: 7.064877918 + -7.25 = -0.185122082
x = -0.185122082

Simplifying
x = -0.185122082


Subproblem 2
x + 7.25 = -7.064877918

Simplifying
x + 7.25 = -7.064877918

Reorder the terms:
7.25 + x = -7.064877918

Solving
7.25 + x = -7.064877918

Solving for variable 'x'.

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

Add '-7.25' to each side of the equation.
7.25 + -7.25 + x = -7.064877918 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -7.064877918 + -7.25
x = -7.064877918 + -7.25

Combine like terms: -7.064877918 + -7.25 = -14.314877918
x = -14.314877918

Simplifying
x = -14.314877918


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.185122082, -14.314877918}

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