Question

2(2x−22)2−5(2x−22)+2=0

Answer 1

Ответ:

2(2x-22)*2-5(2x-22)=-2

(2x*2-5)*(2x-22)=-2

(4-5)*(2x-22)=-2

-1(2x-22)=-2

2x-22=2

2x=2+22

2x=24

x=12

Объяснение:

Answer 2

To solve the quadratic equation $2(2x - 22)^2 - 5(2x - 22) + 2 = 0$, follow these steps:

Step 1: Let $u = 2x - 22$. This substitution will make the equation more manageable.

So the equation becomes: $2u^2 - 5u + 2 = 0$.

Step 2: Factor the quadratic expression if possible. If factoring is not possible, you can use the quadratic formula.

In this case, the quadratic can be factored as $(2u - 1)(u - 2) = 0$.

Step 3: Solve for $u$ using the factored expression:

$2u - 1 = 0$ or $u - 2 = 0$.

Solving for $u$ in the first equation gives $u = \frac{1}{2}$.

Solving for $u$ in the second equation gives $u = 2$.

Step 4: Substitute back the value of $u$ to find the values of $x$:

For $u = \frac{1}{2}$: $2x - 22 = \frac{1}{2}$, $2x = \frac{1}{2} + 22$, $2x = \frac{45}{2}$, $x = \frac{45}{4}$.

For $u = 2$: $2x - 22 = 2$, $2x = 24$, $x = 12$.

So, the solutions for the equation are $x = \frac{45}{4}$ and $x = 12$.