4x^2+20x-29=0

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Solution for 4x^2+20x-29=0 equation: 


Simplifying
4x2 + 20x + -29 = 0

Reorder the terms:
-29 + 20x + 4x2 = 0

Solving
-29 + 20x + 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'.
-7.25 + 5x + x2 = 0

Move the constant term to the right:

Add '7.25' to each side of the equation.
-7.25 + 5x + 7.25 + x2 = 0 + 7.25

Reorder the terms:
-7.25 + 7.25 + 5x + x2 = 0 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + 5x + x2 = 0 + 7.25
5x + x2 = 0 + 7.25

Combine like terms: 0 + 7.25 = 7.25
5x + x2 = 7.25

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 7.25 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 7.25 + 6.25

Combine like terms: 7.25 + 6.25 = 13.5
6.25 + 5x + x2 = 13.5

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 13.5

Calculate the square root of the right side: 3.674234614

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.674234614 and -3.674234614.


Subproblem 1
x + 2.5 = 3.674234614

Simplifying
x + 2.5 = 3.674234614

Reorder the terms:
2.5 + x = 3.674234614

Solving
2.5 + x = 3.674234614

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 3.674234614 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 3.674234614 + -2.5
x = 3.674234614 + -2.5

Combine like terms: 3.674234614 + -2.5 = 1.174234614
x = 1.174234614

Simplifying
x = 1.174234614


Subproblem 2
x + 2.5 = -3.674234614

Simplifying
x + 2.5 = -3.674234614

Reorder the terms:
2.5 + x = -3.674234614

Solving
2.5 + x = -3.674234614

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -3.674234614 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -3.674234614 + -2.5
x = -3.674234614 + -2.5

Combine like terms: -3.674234614 + -2.5 = -6.174234614
x = -6.174234614

Simplifying
x = -6.174234614


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.174234614, -6.174234614}

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