42x^2-69x+20=7x-8

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Solution for 42x^2-69x+20=7x-8 equation: 


Simplifying
42x2 + -69x + 20 = 7x + -8

Reorder the terms:
20 + -69x + 42x2 = 7x + -8

Reorder the terms:
20 + -69x + 42x2 = -8 + 7x

Solving
20 + -69x + 42x2 = -8 + 7x

Solving for variable 'x'.

Reorder the terms:
20 + 8 + -69x + -7x + 42x2 = -8 + 7x + 8 + -7x

Combine like terms: 20 + 8 = 28
28 + -69x + -7x + 42x2 = -8 + 7x + 8 + -7x

Combine like terms: -69x + -7x = -76x
28 + -76x + 42x2 = -8 + 7x + 8 + -7x

Reorder the terms:
28 + -76x + 42x2 = -8 + 8 + 7x + -7x

Combine like terms: -8 + 8 = 0
28 + -76x + 42x2 = 0 + 7x + -7x
28 + -76x + 42x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
28 + -76x + 42x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(14 + -38x + 21x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(14 + -38x + 21x2)' equal to zero and attempt to solve:

Simplifying
14 + -38x + 21x2 = 0

Solving
14 + -38x + 21x2 = 0

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

Divide each side by '21'.
0.6666666667 + -1.80952381x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1.80952381x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1.80952381x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1.80952381x + x2 = 0 + -0.6666666667
-1.80952381x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1.80952381x + x2 = -0.6666666667

The x term is -1.80952381x.  Take half its coefficient (-0.904761905).
Square it (0.8185941047) and add it to both sides.

Add '0.8185941047' to each side of the equation.
-1.80952381x + 0.8185941047 + x2 = -0.6666666667 + 0.8185941047

Reorder the terms:
0.8185941047 + -1.80952381x + x2 = -0.6666666667 + 0.8185941047

Combine like terms: -0.6666666667 + 0.8185941047 = 0.151927438
0.8185941047 + -1.80952381x + x2 = 0.151927438

Factor a perfect square on the left side:
(x + -0.904761905)(x + -0.904761905) = 0.151927438

Calculate the square root of the right side: 0.389778704

Break this problem into two subproblems by setting 
(x + -0.904761905) equal to 0.389778704 and -0.389778704.


Subproblem 1
x + -0.904761905 = 0.389778704

Simplifying
x + -0.904761905 = 0.389778704

Reorder the terms:
-0.904761905 + x = 0.389778704

Solving
-0.904761905 + x = 0.389778704

Solving for variable 'x'.

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

Add '0.904761905' to each side of the equation.
-0.904761905 + 0.904761905 + x = 0.389778704 + 0.904761905

Combine like terms: -0.904761905 + 0.904761905 = 0.000000000
0.000000000 + x = 0.389778704 + 0.904761905
x = 0.389778704 + 0.904761905

Combine like terms: 0.389778704 + 0.904761905 = 1.294540609
x = 1.294540609

Simplifying
x = 1.294540609


Subproblem 2
x + -0.904761905 = -0.389778704

Simplifying
x + -0.904761905 = -0.389778704

Reorder the terms:
-0.904761905 + x = -0.389778704

Solving
-0.904761905 + x = -0.389778704

Solving for variable 'x'.

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

Add '0.904761905' to each side of the equation.
-0.904761905 + 0.904761905 + x = -0.389778704 + 0.904761905

Combine like terms: -0.904761905 + 0.904761905 = 0.000000000
0.000000000 + x = -0.389778704 + 0.904761905
x = -0.389778704 + 0.904761905

Combine like terms: -0.389778704 + 0.904761905 = 0.514983201
x = 0.514983201

Simplifying
x = 0.514983201


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.294540609, 0.514983201}
Solution
x = {1.294540609, 0.514983201}

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