(10x-25)(-6x+28)=6x-17

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Solution for (10x-25)(-6x+28)=6x-17 equation:


Simplifying
(10x + -25)(-6x + 28) = 6x + -17

Reorder the terms:
(-25 + 10x)(-6x + 28) = 6x + -17

Reorder the terms:
(-25 + 10x)(28 + -6x) = 6x + -17

Multiply (-25 + 10x) * (28 + -6x)
(-25(28 + -6x) + 10x * (28 + -6x)) = 6x + -17
((28 * -25 + -6x * -25) + 10x * (28 + -6x)) = 6x + -17
((-700 + 150x) + 10x * (28 + -6x)) = 6x + -17
(-700 + 150x + (28 * 10x + -6x * 10x)) = 6x + -17
(-700 + 150x + (280x + -60x2)) = 6x + -17

Combine like terms: 150x + 280x = 430x
(-700 + 430x + -60x2) = 6x + -17

Reorder the terms:
-700 + 430x + -60x2 = -17 + 6x

Solving
-700 + 430x + -60x2 = -17 + 6x

Solving for variable 'x'.

Reorder the terms:
-700 + 17 + 430x + -6x + -60x2 = -17 + 6x + 17 + -6x

Combine like terms: -700 + 17 = -683
-683 + 430x + -6x + -60x2 = -17 + 6x + 17 + -6x

Combine like terms: 430x + -6x = 424x
-683 + 424x + -60x2 = -17 + 6x + 17 + -6x

Reorder the terms:
-683 + 424x + -60x2 = -17 + 17 + 6x + -6x

Combine like terms: -17 + 17 = 0
-683 + 424x + -60x2 = 0 + 6x + -6x
-683 + 424x + -60x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-683 + 424x + -60x2 = 0

Begin completing the square.  Divide all terms by
-60 the coefficient of the squared term: 

Divide each side by '-60'.
11.38333333 + -7.066666667x + x2 = 0.0

Move the constant term to the right:

Add '-11.38333333' to each side of the equation.
11.38333333 + -7.066666667x + -11.38333333 + x2 = 0.0 + -11.38333333

Reorder the terms:
11.38333333 + -11.38333333 + -7.066666667x + x2 = 0.0 + -11.38333333

Combine like terms: 11.38333333 + -11.38333333 = 0.00000000
0.00000000 + -7.066666667x + x2 = 0.0 + -11.38333333
-7.066666667x + x2 = 0.0 + -11.38333333

Combine like terms: 0.0 + -11.38333333 = -11.38333333
-7.066666667x + x2 = -11.38333333

The x term is -7.066666667x.  Take half its coefficient (-3.533333334).
Square it (12.48444445) and add it to both sides.

Add '12.48444445' to each side of the equation.
-7.066666667x + 12.48444445 + x2 = -11.38333333 + 12.48444445

Reorder the terms:
12.48444445 + -7.066666667x + x2 = -11.38333333 + 12.48444445

Combine like terms: -11.38333333 + 12.48444445 = 1.10111112
12.48444445 + -7.066666667x + x2 = 1.10111112

Factor a perfect square on the left side:
(x + -3.533333334)(x + -3.533333334) = 1.10111112

Calculate the square root of the right side: 1.04933842

Break this problem into two subproblems by setting 
(x + -3.533333334) equal to 1.04933842 and -1.04933842.

Subproblem 1

x + -3.533333334 = 1.04933842 Simplifying x + -3.533333334 = 1.04933842 Reorder the terms: -3.533333334 + x = 1.04933842 Solving -3.533333334 + x = 1.04933842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.533333334' to each side of the equation. -3.533333334 + 3.533333334 + x = 1.04933842 + 3.533333334 Combine like terms: -3.533333334 + 3.533333334 = 0.000000000 0.000000000 + x = 1.04933842 + 3.533333334 x = 1.04933842 + 3.533333334 Combine like terms: 1.04933842 + 3.533333334 = 4.582671754 x = 4.582671754 Simplifying x = 4.582671754

Subproblem 2

x + -3.533333334 = -1.04933842 Simplifying x + -3.533333334 = -1.04933842 Reorder the terms: -3.533333334 + x = -1.04933842 Solving -3.533333334 + x = -1.04933842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.533333334' to each side of the equation. -3.533333334 + 3.533333334 + x = -1.04933842 + 3.533333334 Combine like terms: -3.533333334 + 3.533333334 = 0.000000000 0.000000000 + x = -1.04933842 + 3.533333334 x = -1.04933842 + 3.533333334 Combine like terms: -1.04933842 + 3.533333334 = 2.483994914 x = 2.483994914 Simplifying x = 2.483994914

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.582671754, 2.483994914}

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