Question

24x-6x(13x-9)=-13-13x(6x-1)

Answer 1

24x-78x+54x=-13-78x+13x
24x-78x+54x+78x-13x=-13
24x+54x-13x=13
65x=13
x=13/65
x= 1/5

Answer 2

Let's simplify the equation step by step:

24x - 6x(13x - 9) = -13 - 13x(6x - 1)

First, let's distribute the terms inside the parentheses:

24x - 6x * 13x + 6x * 9 = -13 - 13x * 6x + 13x * 1

Simplifying further:

24x - 78x^2 + 54x = -13 - 78x^2 + 13x

Rearranging the terms:

24x - 78x^2 + 54x + 78x^2 - 13x = -13

Combining like terms:

65x - 78x^2 = -13

Moving all terms to one side to set the equation to zero:

78x^2 - 65x + 13 = 0

Now, we have a quadratic equation in standard form. To solve it, we can use factoring, completing the square, or the quadratic formula.

Unfortunately, this quadratic equation does not factor easily. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 78, b = -65, and c = 13.

x = (-(-65) ± √((-65)^2 - 4 * 78 * 13)) / (2 * 78)

x = (65 ± √(4225 - 4056)) / 156

x = (65 ± √169) / 156

x = (65 ± 13) / 156

So, the solutions are:

x = (65 + 13) / 156 = 78 / 156 = 1/2

x = (65 - 13) / 156 = 52 / 156 = 1/3

Therefore, the equation 24x - 6x(13x - 9) = -13 - 13x(6x - 1) has two solutions: x = 1/2 and x = 1/3.