x(3x-5)=26

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Solution for x(3x-5)=26 equation: 


Simplifying
x(3x + -5) = 26

Reorder the terms:
x(-5 + 3x) = 26
(-5 * x + 3x * x) = 26
(-5x + 3x2) = 26

Solving
-5x + 3x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + -5x + 3x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + -5x + 3x2 = 0

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

Divide each side by '3'.
-8.666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '8.666666667' to each side of the equation.
-8.666666667 + -1.666666667x + 8.666666667 + x2 = 0 + 8.666666667

Reorder the terms:
-8.666666667 + 8.666666667 + -1.666666667x + x2 = 0 + 8.666666667

Combine like terms: -8.666666667 + 8.666666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 8.666666667
-1.666666667x + x2 = 0 + 8.666666667

Combine like terms: 0 + 8.666666667 = 8.666666667
-1.666666667x + x2 = 8.666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 8.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 8.666666667 + 0.6944444447

Combine like terms: 8.666666667 + 0.6944444447 = 9.3611111117
0.6944444447 + -1.666666667x + x2 = 9.3611111117

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 9.3611111117

Calculate the square root of the right side: 3.059593292

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 3.059593292 and -3.059593292.


Subproblem 1
x + -0.8333333335 = 3.059593292

Simplifying
x + -0.8333333335 = 3.059593292

Reorder the terms:
-0.8333333335 + x = 3.059593292

Solving
-0.8333333335 + x = 3.059593292

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 3.059593292 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 3.059593292 + 0.8333333335
x = 3.059593292 + 0.8333333335

Combine like terms: 3.059593292 + 0.8333333335 = 3.8929266255
x = 3.8929266255

Simplifying
x = 3.8929266255


Subproblem 2
x + -0.8333333335 = -3.059593292

Simplifying
x + -0.8333333335 = -3.059593292

Reorder the terms:
-0.8333333335 + x = -3.059593292

Solving
-0.8333333335 + x = -3.059593292

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -3.059593292 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -3.059593292 + 0.8333333335
x = -3.059593292 + 0.8333333335

Combine like terms: -3.059593292 + 0.8333333335 = -2.2262599585
x = -2.2262599585

Simplifying
x = -2.2262599585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.8929266255, -2.2262599585}

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