Question

(2x-1)^2-6(6-x)=2x (x+2)(x-3)-(x-5)(5x+5)=x^2-x

Answer 1

Ответ:

(2х-1)^2-6(6-х)=2х

2х^2-4х+1-36+6х=2х

4х^2-35=0

х^2=35/4

$x = \frac{ \sqrt{35} }{2} \: \: \: x = \frac{ \sqrt{35} }{2}$

(х+2)(х-3)-(х-5)(5х+5)=х^2-х

х^2-3х+2х-6-(5х^2-20х-25)=х^2-х

-3х+2х-6-5х^2+20х+25=-х

19х+19-5х^2=-х

5х^2-20х-19=0

$x = \frac{10 + \sqrt{195} }{5} \: \: \: \: \: x = \frac{10 - \sqrt{195} }{5}$

Answer 2

Let's solve each of these equations step by step:

1. (2x - 1)^2 - 6(6 - x) = 2x

Expand the left side of the equation:

(2x - 1)^2 = (2x - 1)(2x - 1) = 4x^2 - 4x + 1

Now, distribute the -6 on the right side of the equation:

-6(6 - x) = -6(6) + 6x = -36 + 6x

So, the equation becomes:

4x^2 - 4x + 1 - 36 + 6x = 2x

Now, combine like terms on the left side:

4x^2 + 2x - 35 = 2x

Subtract 2x from both sides:

4x^2 - 35 = 0

Now, add 35 to both sides:

4x^2 = 35

Divide both sides by 4:

x^2 = 35/4

Take the square root of both sides:

x = ±√(35/4)

x = ±(√35/2)

So, the solutions to the first equation are:

x = √(35/2) and x = -√(35/2)

2. (x+2)(x-3) - (x-5)(5x+5) = x^2 - x

Expand both sides of the equation:

(x+2)(x-3) - (x-5)(5x+5) = x^2 - x

(x^2 - 3x + 2x - 6) - (5x^2 - 5x - 25x + 25) = x^2 - x

Now, simplify both sides by combining like terms:

(x^2 - x - 6) - (5x^2 - 30x + 25) = x^2 - x

Now, distribute the negative sign on the left side:

x^2 - x - 6 - 5x^2 + 30x - 25 = x^2 - x

Combine like terms:

(-4x^2 + 29x - 31) = x^2 - x

Now, move all terms to one side of the equation:

-4x^2 + 29x - 31 - x^2 + x = 0

Combine like terms again:

-5x^2 + 30x - 31 = 0

Divide the entire equation by -1 to simplify:

5x^2 - 30x + 31 = 0

This is a quadratic equation. You can use the quadratic formula to find its solutions:

x = (-b ± √(b² - 4ac)) / (2a)

In this case, a = 5, b = -30, and c = 31. Plug these values into the quadratic formula:

x = (-(-30) ± √((-30)² - 4 * 5 * 31)) / (2 * 5)

x = (30 ± √(900 - 620)) / 10

x = (30 ± √280) / 10

x = (30 ± 2√70) / 10

Now, simplify:

x = (3 ± √70)/1

So, the solutions to the second equation are:

x = 3 + √70 and x = 3 - √70