4x^2-70x+60=0

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Solution for 4x^2-70x+60=0 equation: 


Simplifying
4x2 + -70x + 60 = 0

Reorder the terms:
60 + -70x + 4x2 = 0

Solving
60 + -70x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + -35x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + -35x + 2x2)' equal to zero and attempt to solve:

Simplifying
30 + -35x + 2x2 = 0

Solving
30 + -35x + 2x2 = 0

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

Divide each side by '2'.
15 + -17.5x + x2 = 0

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -17.5x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -17.5x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -17.5x + x2 = 0 + -15
-17.5x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-17.5x + x2 = -15

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 = -15 + 76.5625

Reorder the terms:
76.5625 + -17.5x + x2 = -15 + 76.5625

Combine like terms: -15 + 76.5625 = 61.5625
76.5625 + -17.5x + x2 = 61.5625

Factor a perfect square on the left side:
(x + -8.75)(x + -8.75) = 61.5625

Calculate the square root of the right side: 7.846177413

Break this problem into two subproblems by setting 
(x + -8.75) equal to 7.846177413 and -7.846177413.


Subproblem 1
x + -8.75 = 7.846177413

Simplifying
x + -8.75 = 7.846177413

Reorder the terms:
-8.75 + x = 7.846177413

Solving
-8.75 + x = 7.846177413

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 = 7.846177413 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = 7.846177413 + 8.75
x = 7.846177413 + 8.75

Combine like terms: 7.846177413 + 8.75 = 16.596177413
x = 16.596177413

Simplifying
x = 16.596177413


Subproblem 2
x + -8.75 = -7.846177413

Simplifying
x + -8.75 = -7.846177413

Reorder the terms:
-8.75 + x = -7.846177413

Solving
-8.75 + x = -7.846177413

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 = -7.846177413 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = -7.846177413 + 8.75
x = -7.846177413 + 8.75

Combine like terms: -7.846177413 + 8.75 = 0.903822587
x = 0.903822587

Simplifying
x = 0.903822587


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.596177413, 0.903822587}
Solution
x = {16.596177413, 0.903822587}

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