Question

2(5x−23)2−8(5x−23)+8=0 x1-? x2-?

Answer 1

20•x-8(5•x-23)-84=20•x+-40•x+184-84-20•x+100

Answer 2

To solve the quadratic equation, let's simplify it first:

2(5x - 23)^2 - 8(5x - 23) + 8 = 0

Let's denote y = (5x - 23):

2y^2 - 8y + 8 = 0

Now, we can solve this quadratic equation by applying the quadratic formula:

y = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = -8, and c = 8. Substituting these values into the quadratic formula:

y = (-(-8) ± √((-8)^2 - 4 * 2 * 8)) / (2 * 2) = (8 ± √(64 - 64)) / 4 = (8 ± √0) / 4

Since the discriminant (b^2 - 4ac) is zero, the quadratic equation has only one real root.

Therefore, y = 8/4 = 2.

Now, we can substitute y back in to find x:

5x - 23 = 2

Adding 23 to both sides:

5x = 2 + 23 5x = 25

Dividing both sides by 5:

x = 25/5 x = 5

So, the solution to the equation is x = 5.