Question

2(2x−11)^2−10(2x−11)+8=0

Answer 1

Ответ:

x1=6 x2=15/2

Объяснение:

Answer 2

To solve the equation 2(2x−11)^2−10(2x−11)+8=0, we can use a variable substitution. Let's set y = 2x - 11 to simplify the equation:

2y^2 - 10y + 8 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Let's factor the equation:

2y^2 - 10y + 8 = 0

2(y^2 - 5y + 4) = 0

2(y - 1)(y - 4) = 0

Setting each factor equal to zero:

y - 1 = 0 or y - 4 = 0

Solving for y in each case:

y = 1 or y = 4

Now substitute back y = 2x - 11:

2x - 11 = 1 or 2x - 11 = 4

Solving for x in each case:

2x = 1 + 11 or 2x = 4 + 11

2x = 12 or 2x = 15

x = 6 or x = 7.5

Therefore, the solutions to the equation 2(2x−11)^2−10(2x−11)+8=0 are x = 6 and x = 7.5.