4x^2+29x-1=0

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Solution for 4x^2+29x-1=0 equation: 


Simplifying
4x2 + 29x + -1 = 0

Reorder the terms:
-1 + 29x + 4x2 = 0

Solving
-1 + 29x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
-0.25 + 7.25x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 7.25x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + 7.25x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 7.25x + x2 = 0 + 0.25
7.25x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
7.25x + x2 = 0.25

The x term is 7.25x.  Take half its coefficient (3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
7.25x + 13.140625 + x2 = 0.25 + 13.140625

Reorder the terms:
13.140625 + 7.25x + x2 = 0.25 + 13.140625

Combine like terms: 0.25 + 13.140625 = 13.390625
13.140625 + 7.25x + x2 = 13.390625

Factor a perfect square on the left side:
(x + 3.625)(x + 3.625) = 13.390625

Calculate the square root of the right side: 3.659320292

Break this problem into two subproblems by setting 
(x + 3.625) equal to 3.659320292 and -3.659320292.


Subproblem 1
x + 3.625 = 3.659320292

Simplifying
x + 3.625 = 3.659320292

Reorder the terms:
3.625 + x = 3.659320292

Solving
3.625 + x = 3.659320292

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = 3.659320292 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = 3.659320292 + -3.625
x = 3.659320292 + -3.625

Combine like terms: 3.659320292 + -3.625 = 0.034320292
x = 0.034320292

Simplifying
x = 0.034320292


Subproblem 2
x + 3.625 = -3.659320292

Simplifying
x + 3.625 = -3.659320292

Reorder the terms:
3.625 + x = -3.659320292

Solving
3.625 + x = -3.659320292

Solving for variable 'x'.

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

Add '-3.625' to each side of the equation.
3.625 + -3.625 + x = -3.659320292 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + x = -3.659320292 + -3.625
x = -3.659320292 + -3.625

Combine like terms: -3.659320292 + -3.625 = -7.284320292
x = -7.284320292

Simplifying
x = -7.284320292


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.034320292, -7.284320292}

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