Question

X2 + 45x = -200 Using the quadratic formual and the discirimnat

Answer 1

Answer:

Positive discriminant = 2 real solution

x= -5,-40

Step-by-step explanation:

The discriminant is used to see how many solutions an equation has. If it is negative, the equation has no real solutions, if =0 the equation has 1, and if it is positive, the equation has two real solutions.

The discriminant is the part of the quadratic formula inside the square root:

$b^{2}-4ac$

Every quadratic formula has the structure:

$ax^{2} +bx+c=0$

So first, in order to meet this structure we need to add 200 to both sides so the equation is equal to 0. This gives us:

$x^{2} +45x+200=0$

Our a=1, b=45 and c=200

Now we can substitute these values into the discriminant:

$(45)^{2} -4(1)(200)$

Solve:

$2025-800=1225$

The discriminant is a positive number which means this equation will have 2 real solution. Now we just need to plug in our values into the quadratic formula to solve this equation. Quadratic formula:

$x=\frac{-+/-\sqrt{b^{2}-4ac} }{2a} \\x=\frac{-45+/-\sqrt{1225} }{2}$

(Same discriminant value)

$x=\frac{-45+/-35}{2}$

Now to find the two solutions, we use both signs in the equation. Solution 1:

$x=\frac{-45+35}{2}$

$x=\frac{-10}{2}=-5$

Our first solution is -5, now for the second:

$x=\frac{-45-35}{2}\\\\ x=\frac{-80}{2}=-40$

The two solution to this equation are -5 and -40.

Hope this helped!