Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

Solve this quadratic equation.

x 2 + 5x + 3 = 0

Answer 1

5x^2-3 is the anwser

Answer 2

`x_(1) \approx -0.70`

`x_(2) \approx -4.30`

Explanation:

The given equation is:
`x^(2)+5x+3=0`

To find the solution of any quadratic equation we use:

`x_(1,2)=\frac{-b \±\sqrt{b^(2)-4ac} }{2a}`

Where:

`a:` is the coefficient of the quadratic term.

`b:` is the coefficient of the linear term.

`c:` is the independent term.

So, according to this, each variables is equal to:

`a=1`

`b=5`

`c=3`

Now, we substitute these values in the formula:

`x_(1,2)=\frac{-5 \±\sqrt{(5)^(2)-4(1)(3)} }{2(1)}`

`x_(1,2)=(-5 \±√(25-12) )/(2)`

`x_(1,2)=(-5 \±√(13) )/(2)`

`x_(1,2)=(-5 \±√(13) )/(2)`

So, one solution has the positive sign, and the other the negative sign. Therefore the solutions are:

`x_(1)=(-5 +√(13) )/(2) \approx -0.70`

`x_(2)=(-5 -√(13) )/(2) \approx -4.30`

As you can see, the solution was founded just by using the formula, identifying the values of a, b and c. Then, solving the formula we all values replaced.