Question

2(4x−12)2−7(4x−12)+6=0

Answer 1

2(4x - 12)² - 7(4x - 12) + 6 = 0

Сделаем замену :

4x - 12 = m

2m² - 7m + 6 = 0

D = (- 7)² - 4 * 2 * 6 = 49 - 48 = 1

$m_{1}=\frac{7-1}{4}=1,5\\\\m_{2}=\frac{7+1}{4}=2\\\\1)4x-12=1,5\\\\4x=13,5\\\\x_{1}=3,375\\\\2)4x-12=2\\\\4x=14\\\\x_{2}=3,5\\\\Otvet:\boxed{3,375;3,5}$

Answer 2

To solve the quadratic equation 2(4x−12)^2−7(4x−12)+6=0, we can use the quadratic formula or factorization method. Let's use the factorization method.

Given equation: 2(4x−12)^2 − 7(4x−12) + 6 = 0

Let's start by factoring out the common term (4x−12):

(4x−12) is common to all terms, so factor it out:

2(4x−12)^2 − 7(4x−12) + 6 = (4x−12)(2(4x−12) − 7) + 6 = 0

Now we have a quadratic expression in the form of a binomial multiplied by another expression. Let's simplify the second factor inside the parentheses:

2(4x−12) − 7 = 8x − 24 − 7 = 8x − 31

So, the equation becomes:

(4x−12)(8x−31) + 6 = 0

Now we have factored the equation into two binomial factors:

(4x−12)(8x−31) + 6 = 0

Now, set each factor equal to zero and solve for x:

4x − 12 = 0 or 8x − 31 = 0

Solve for x in each equation:

4x = 12 or 8x = 31

x = 3 or x = 31/8

So, the solutions to the quadratic equation are x = 3 and x = 31/8.