Question

X2 - 16X2 + 59X - 44 = 0

Answer 1

x²-16x²+59x-44=0
-15x²+59x-44=0
d=b²-4ac=59²-4*(-15)*(-44)=3481-2640=841
√d=√841=29
x1=(-b+√d)/2a=(-59+29)/2*(-15)=-30/-30=1
x2=(-b-√d)/2a=(-59-29)/2*(-15)=-88/-30=2,93333
Ответ:x1=1;x2=2,93333

Answer 2

To solve the quadratic equation x^2 - 16x^2 + 59x - 44 = 0, follow these steps:

1. Combine like terms:

x^2 - 16x^2 + 59x - 44 = 0

-15x^2 + 59x - 44 = 0

2. To make the equation easier to work with, you can multiply the entire equation by -1 to change the signs of all the terms:

15x^2 - 59x + 44 = 0

3. Now, let's solve for x. You can either use the quadratic formula or try to factor the quadratic expression. In this case, it's easier to factor:

The factors of 15x^2 are (3x)(5x). The factors of 44 are (4)(11).

Now, we need to find two numbers whose product is 15 * 44 = 660 and whose sum is -59 (the coefficient of the middle term, -59x). These numbers are -55 and -4 because (-55) * (-4) = 220 and (-55) + (-4) = -59.

So, you can rewrite the middle term, -59x, as -55x - 4x:

15x^2 - 55x - 4x + 44 = 0

4. Group and factor by grouping:

(15x^2 - 55x) - (4x - 44) = 0

5x(3x - 11) - 4(3x - 11) = 0

Now, notice that (3x - 11) is a common factor:

(3x - 11)(5x - 4) = 0

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

3x - 11 = 0 5x - 4 = 0

For the first equation, add 11 to both sides:

3x = 11

Now, divide by 3:

x = 11/3

For the second equation, add 4 to both sides:

5x = 4

Now, divide by 5:

x = 4/5

So, the solutions for the equation are:

x = 11/3 and x = 4/5.