Question

Решить уравнение (5х-1)(х+2)+3(х-4)(4+4)=2(2х+3)^2-8

Answer 1

5x^2 +9x-2-24x-96=8x^2+24x+18-8

3x^2+39x+108=0

x^2+13x+36=0

D=25

x=(-13+5)÷2=-4

x=(-13-5)÷2=-9

Answer 2

To solve the equation (5x-1)(x+2) + 3(x-4)(4+4) = 2(2x+3)^2 - 8, we'll first simplify both sides of the equation and then find the value(s) of x that satisfy the equation.

Step 1: Simplify the equation

(5x-1)(x+2) + 3(x-4)(4+4) = 2(2x+3)^2 - 8

Expand each term:

(5x^2 + 9x - 2) + 3(x-4)(8) = 2(4x^2 + 12x + 9) - 8

(5x^2 + 9x - 2) + 24(x-4) = 8x^2 + 24x + 18 - 8

Step 2: Continue simplifying

Expand the second term:

(5x^2 + 9x - 2) + 24x - 96 = 8x^2 + 24x + 10

Combine like terms:

5x^2 + 9x + 24x - 2 - 96 = 8x^2 + 24x + 10

5x^2 + 33x - 98 = 8x^2 + 24x + 10

Step 3: Move all terms to one side of the equation to set it to zero:

5x^2 + 33x - 98 - 8x^2 - 24x - 10 = 0

Combine like terms:

5x^2 - 8x^2 + 33x - 24x - 98 - 10 = 0

-3x^2 + 9x - 108 = 0

Step 4: Now, let's solve the quadratic equation for x. We can either factor it or use the quadratic formula.

Using the quadratic formula:

The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / 2a

For the equation -3x^2 + 9x - 108 = 0:

a = -3 b = 9 c = -108

x = (-(9) ± √((9)^2 - 4*(-3)(-108))) / 2(-3)

x = (-9 ± √(81 - 1296)) / -6

x = (-9 ± √(-1215)) / -6

Since the discriminant (b^2 - 4ac) is negative, there are no real solutions for x. The equation has complex solutions.

So, the solution to the equation is:

x = (-9 ± √(-1215)) / -6

x = (-9 ± √(1215)i) / -6

x = (9 ± √1215i) / 6

x = (9 ± 3√135i) / 6

x = (3/2) ± (1/2)√135i

where "i" is the imaginary unit, √135 is the square root of 135, and ± indicates two possible solutions.