Question

Прошу помогите решите уравнение 2x^2+3x=0 ЗАРАНЕЕ СПАСИБО)))

Answer 1

X(2x+3)=0  
x=0 или 2x+3=0
              2x=-3
              x=-1,5

Answer 2

2х^2 + 3x =0
x(2x+3)=0
x=0
2x+3=0
2x=-3
x= -3/2=-1,5

Answer 3

Solving the Equation 2x^2 + 3x = 0

To solve the equation 2x^2 + 3x = 0, we can use the factoring method or the quadratic formula. Let's solve it using both methods.

Factoring Method

To factor the quadratic equation 2x^2 + 3x = 0, we can factor out the common term x:

2x(x + 3/2) = 0

Now, we can solve for x by setting each factor equal to zero:

1. 2x = 0 2. x + 3/2 = 0

Solving for x in each equation gives us:

1. x = 0 2. x = -3/2

So, the solutions to the equation 2x^2 + 3x = 0 are x = 0 and x = -3/2.

Quadratic Formula

We can also solve the equation using the quadratic formula, which states that for the quadratic equation ax^2 + bx + c = 0, the solutions for x are given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation 2x^2 + 3x = 0, we have: - a = 2 - b = 3 - c = 0

Plugging these values into the quadratic formula gives us:

x = (-3 ± √(3^2 - 4*2*0)) / (2*2) x = (-3 ± √(9)) / 4 x = (-3 ± 3) / 4

So, the solutions are: - x = (-3 + 3) / 4 = 0 / 4 = 0 - x = (-3 - 3) / 4 = -6 / 4 = -3/2

Therefore, the solutions obtained using the factoring method and the quadratic formula are consistent, and the solutions to the equation 2x^2 + 3x = 0 are x = 0 and x = -3/2.