8x(3x-10)=35

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Solution for 8x(3x-10)=35 equation: 


Simplifying
8x(3x + -10) = 35

Reorder the terms:
8x(-10 + 3x) = 35
(-10 * 8x + 3x * 8x) = 35
(-80x + 24x2) = 35

Solving
-80x + 24x2 = 35

Solving for variable 'x'.

Reorder the terms:
-35 + -80x + 24x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-35 + -80x + 24x2 = 0

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

Divide each side by '24'.
-1.458333333 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '1.458333333' to each side of the equation.
-1.458333333 + -3.333333333x + 1.458333333 + x2 = 0 + 1.458333333

Reorder the terms:
-1.458333333 + 1.458333333 + -3.333333333x + x2 = 0 + 1.458333333

Combine like terms: -1.458333333 + 1.458333333 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + 1.458333333
-3.333333333x + x2 = 0 + 1.458333333

Combine like terms: 0 + 1.458333333 = 1.458333333
-3.333333333x + x2 = 1.458333333

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 1.458333333 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 1.458333333 + 2.777777779

Combine like terms: 1.458333333 + 2.777777779 = 4.236111112
2.777777779 + -3.333333333x + x2 = 4.236111112

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 4.236111112

Calculate the square root of the right side: 2.058181506

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.058181506 and -2.058181506.


Subproblem 1
x + -1.666666667 = 2.058181506

Simplifying
x + -1.666666667 = 2.058181506

Reorder the terms:
-1.666666667 + x = 2.058181506

Solving
-1.666666667 + x = 2.058181506

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.058181506 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.058181506 + 1.666666667
x = 2.058181506 + 1.666666667

Combine like terms: 2.058181506 + 1.666666667 = 3.724848173
x = 3.724848173

Simplifying
x = 3.724848173


Subproblem 2
x + -1.666666667 = -2.058181506

Simplifying
x + -1.666666667 = -2.058181506

Reorder the terms:
-1.666666667 + x = -2.058181506

Solving
-1.666666667 + x = -2.058181506

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.058181506 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.058181506 + 1.666666667
x = -2.058181506 + 1.666666667

Combine like terms: -2.058181506 + 1.666666667 = -0.391514839
x = -0.391514839

Simplifying
x = -0.391514839


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.724848173, -0.391514839}

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