4x^2-70x+6=0

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Solution for 4x^2-70x+6=0 equation: 


Simplifying
4x2 + -70x + 6 = 0

Reorder the terms:
6 + -70x + 4x2 = 0

Solving
6 + -70x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(3 + -35x + 2x2)' equal to zero and attempt to solve:

Simplifying
3 + -35x + 2x2 = 0

Solving
3 + -35x + 2x2 = 0

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

Divide each side by '2'.
1.5 + -17.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -17.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -17.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -17.5x + x2 = 0 + -1.5
-17.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-17.5x + x2 = -1.5

The x term is -17.5x.  Take half its coefficient (-8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
-17.5x + 76.5625 + x2 = -1.5 + 76.5625

Reorder the terms:
76.5625 + -17.5x + x2 = -1.5 + 76.5625

Combine like terms: -1.5 + 76.5625 = 75.0625
76.5625 + -17.5x + x2 = 75.0625

Factor a perfect square on the left side:
(x + -8.75)(x + -8.75) = 75.0625

Calculate the square root of the right side: 8.663861726

Break this problem into two subproblems by setting 
(x + -8.75) equal to 8.663861726 and -8.663861726.


Subproblem 1
x + -8.75 = 8.663861726

Simplifying
x + -8.75 = 8.663861726

Reorder the terms:
-8.75 + x = 8.663861726

Solving
-8.75 + x = 8.663861726

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = 8.663861726 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = 8.663861726 + 8.75
x = 8.663861726 + 8.75

Combine like terms: 8.663861726 + 8.75 = 17.413861726
x = 17.413861726

Simplifying
x = 17.413861726


Subproblem 2
x + -8.75 = -8.663861726

Simplifying
x + -8.75 = -8.663861726

Reorder the terms:
-8.75 + x = -8.663861726

Solving
-8.75 + x = -8.663861726

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = -8.663861726 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = -8.663861726 + 8.75
x = -8.663861726 + 8.75

Combine like terms: -8.663861726 + 8.75 = 0.086138274
x = 0.086138274

Simplifying
x = 0.086138274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.413861726, 0.086138274}
Solution
x = {17.413861726, 0.086138274}

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