5x^2+20x-335=0

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Solution for 5x^2+20x-335=0 equation: 


Simplifying
5x2 + 20x + -335 = 0

Reorder the terms:
-335 + 20x + 5x2 = 0

Solving
-335 + 20x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-67 + 4x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-67 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-67 + 4x + x2 = 0

Solving
-67 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '67' to each side of the equation.
-67 + 4x + 67 + x2 = 0 + 67

Reorder the terms:
-67 + 67 + 4x + x2 = 0 + 67

Combine like terms: -67 + 67 = 0
0 + 4x + x2 = 0 + 67
4x + x2 = 0 + 67

Combine like terms: 0 + 67 = 67
4x + x2 = 67

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 67 + 4

Reorder the terms:
4 + 4x + x2 = 67 + 4

Combine like terms: 67 + 4 = 71
4 + 4x + x2 = 71

Factor a perfect square on the left side:
(x + 2)(x + 2) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + 2) equal to 8.426149773 and -8.426149773.


Subproblem 1
x + 2 = 8.426149773

Simplifying
x + 2 = 8.426149773

Reorder the terms:
2 + x = 8.426149773

Solving
2 + x = 8.426149773

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 8.426149773 + -2

Combine like terms: 2 + -2 = 0
0 + x = 8.426149773 + -2
x = 8.426149773 + -2

Combine like terms: 8.426149773 + -2 = 6.426149773
x = 6.426149773

Simplifying
x = 6.426149773


Subproblem 2
x + 2 = -8.426149773

Simplifying
x + 2 = -8.426149773

Reorder the terms:
2 + x = -8.426149773

Solving
2 + x = -8.426149773

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -8.426149773 + -2

Combine like terms: 2 + -2 = 0
0 + x = -8.426149773 + -2
x = -8.426149773 + -2

Combine like terms: -8.426149773 + -2 = -10.426149773
x = -10.426149773

Simplifying
x = -10.426149773


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.426149773, -10.426149773}
Solution
x = {6.426149773, -10.426149773}

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