38x(x-14)=62

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Solution for 38x(x-14)=62 equation: 


Simplifying
38x(x + -14) = 62

Reorder the terms:
38x(-14 + x) = 62
(-14 * 38x + x * 38x) = 62
(-532x + 38x2) = 62

Solving
-532x + 38x2 = 62

Solving for variable 'x'.

Reorder the terms:
-62 + -532x + 38x2 = 62 + -62

Combine like terms: 62 + -62 = 0
-62 + -532x + 38x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-31 + -266x + 19x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-31 + -266x + 19x2)' equal to zero and attempt to solve:

Simplifying
-31 + -266x + 19x2 = 0

Solving
-31 + -266x + 19x2 = 0

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

Divide each side by '19'.
-1.631578947 + -14x + x2 = 0

Move the constant term to the right:

Add '1.631578947' to each side of the equation.
-1.631578947 + -14x + 1.631578947 + x2 = 0 + 1.631578947

Reorder the terms:
-1.631578947 + 1.631578947 + -14x + x2 = 0 + 1.631578947

Combine like terms: -1.631578947 + 1.631578947 = 0.000000000
0.000000000 + -14x + x2 = 0 + 1.631578947
-14x + x2 = 0 + 1.631578947

Combine like terms: 0 + 1.631578947 = 1.631578947
-14x + x2 = 1.631578947

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 1.631578947 + 49

Reorder the terms:
49 + -14x + x2 = 1.631578947 + 49

Combine like terms: 1.631578947 + 49 = 50.631578947
49 + -14x + x2 = 50.631578947

Factor a perfect square on the left side:
(x + -7)(x + -7) = 50.631578947

Calculate the square root of the right side: 7.115587042

Break this problem into two subproblems by setting 
(x + -7) equal to 7.115587042 and -7.115587042.


Subproblem 1
x + -7 = 7.115587042

Simplifying
x + -7 = 7.115587042

Reorder the terms:
-7 + x = 7.115587042

Solving
-7 + x = 7.115587042

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 7.115587042 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.115587042 + 7
x = 7.115587042 + 7

Combine like terms: 7.115587042 + 7 = 14.115587042
x = 14.115587042

Simplifying
x = 14.115587042


Subproblem 2
x + -7 = -7.115587042

Simplifying
x + -7 = -7.115587042

Reorder the terms:
-7 + x = -7.115587042

Solving
-7 + x = -7.115587042

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -7.115587042 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.115587042 + 7
x = -7.115587042 + 7

Combine like terms: -7.115587042 + 7 = -0.115587042
x = -0.115587042

Simplifying
x = -0.115587042


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.115587042, -0.115587042}
Solution
x = {14.115587042, -0.115587042}

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