4x^2-74x-20=0

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Solution for 4x^2-74x-20=0 equation: 


Simplifying
4x2 + -74x + -20 = 0

Reorder the terms:
-20 + -74x + 4x2 = 0

Solving
-20 + -74x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -37x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + -37x + 2x2)' equal to zero and attempt to solve:

Simplifying
-10 + -37x + 2x2 = 0

Solving
-10 + -37x + 2x2 = 0

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

Divide each side by '2'.
-5 + -18.5x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -18.5x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -18.5x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -18.5x + x2 = 0 + 5
-18.5x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-18.5x + x2 = 5

The x term is -18.5x.  Take half its coefficient (-9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
-18.5x + 85.5625 + x2 = 5 + 85.5625

Reorder the terms:
85.5625 + -18.5x + x2 = 5 + 85.5625

Combine like terms: 5 + 85.5625 = 90.5625
85.5625 + -18.5x + x2 = 90.5625

Factor a perfect square on the left side:
(x + -9.25)(x + -9.25) = 90.5625

Calculate the square root of the right side: 9.516433155

Break this problem into two subproblems by setting 
(x + -9.25) equal to 9.516433155 and -9.516433155.


Subproblem 1
x + -9.25 = 9.516433155

Simplifying
x + -9.25 = 9.516433155

Reorder the terms:
-9.25 + x = 9.516433155

Solving
-9.25 + x = 9.516433155

Solving for variable 'x'.

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

Add '9.25' to each side of the equation.
-9.25 + 9.25 + x = 9.516433155 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + x = 9.516433155 + 9.25
x = 9.516433155 + 9.25

Combine like terms: 9.516433155 + 9.25 = 18.766433155
x = 18.766433155

Simplifying
x = 18.766433155


Subproblem 2
x + -9.25 = -9.516433155

Simplifying
x + -9.25 = -9.516433155

Reorder the terms:
-9.25 + x = -9.516433155

Solving
-9.25 + x = -9.516433155

Solving for variable 'x'.

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

Add '9.25' to each side of the equation.
-9.25 + 9.25 + x = -9.516433155 + 9.25

Combine like terms: -9.25 + 9.25 = 0.00
0.00 + x = -9.516433155 + 9.25
x = -9.516433155 + 9.25

Combine like terms: -9.516433155 + 9.25 = -0.266433155
x = -0.266433155

Simplifying
x = -0.266433155


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.766433155, -0.266433155}
Solution
x = {18.766433155, -0.266433155}

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