2x^2+29x-6.3=0

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Solution for 2x^2+29x-6.3=0 equation: 


Simplifying
2x2 + 29x + -6.3 = 0

Reorder the terms:
-6.3 + 29x + 2x2 = 0

Solving
-6.3 + 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'.
-3.15 + 14.5x + x2 = 0

Move the constant term to the right:

Add '3.15' to each side of the equation.
-3.15 + 14.5x + 3.15 + x2 = 0 + 3.15

Reorder the terms:
-3.15 + 3.15 + 14.5x + x2 = 0 + 3.15

Combine like terms: -3.15 + 3.15 = 0.00
0.00 + 14.5x + x2 = 0 + 3.15
14.5x + x2 = 0 + 3.15

Combine like terms: 0 + 3.15 = 3.15
14.5x + x2 = 3.15

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 = 3.15 + 52.5625

Reorder the terms:
52.5625 + 14.5x + x2 = 3.15 + 52.5625

Combine like terms: 3.15 + 52.5625 = 55.7125
52.5625 + 14.5x + x2 = 55.7125

Factor a perfect square on the left side:
(x + 7.25)(x + 7.25) = 55.7125

Calculate the square root of the right side: 7.464080653

Break this problem into two subproblems by setting 
(x + 7.25) equal to 7.464080653 and -7.464080653.


Subproblem 1
x + 7.25 = 7.464080653

Simplifying
x + 7.25 = 7.464080653

Reorder the terms:
7.25 + x = 7.464080653

Solving
7.25 + x = 7.464080653

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 = 7.464080653 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = 7.464080653 + -7.25
x = 7.464080653 + -7.25

Combine like terms: 7.464080653 + -7.25 = 0.214080653
x = 0.214080653

Simplifying
x = 0.214080653


Subproblem 2
x + 7.25 = -7.464080653

Simplifying
x + 7.25 = -7.464080653

Reorder the terms:
7.25 + x = -7.464080653

Solving
7.25 + x = -7.464080653

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 = -7.464080653 + -7.25

Combine like terms: 7.25 + -7.25 = 0.00
0.00 + x = -7.464080653 + -7.25
x = -7.464080653 + -7.25

Combine like terms: -7.464080653 + -7.25 = -14.714080653
x = -14.714080653

Simplifying
x = -14.714080653


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.214080653, -14.714080653}

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