Question

x^2+5x-24 = 0
+ 24 +24
x^2+5x=24
Then I know you square root both sides but that's when I get stuck, I'm thinking it would then be something like
x + ? = 2sqrt6
The answer is -5 so I just need help being taught how to do these last steps, unless I'm completely wrong in the beginning steps.

Answer 1

Are you attempting to solve for x using the complete the square method?

Answer 2

I'm trying to get the sum of 2 solutions of the equation \[X^{2}+5x-24=0\]

Answer 3

you mean the product of two solutions, in other words you want to factorise the quadratic

Answer 4

(x+a)(x+b) = x^2 +5x -24

Answer 5

Solve the equation using the complete the square method. Then add the two solutions together. The final answer is indeed -5. Now just explain how to do it.

Answer 6

Hmm. I don't get -5 as one of the solutions?

Answer 7

Step 1.
Let's solve the quadratic equation using the complete the square method.
\(x^2+5x-24 ~~~= ~~~0\)
\(~~~~~~~~~~~~+24~~~~+24\)
--------------------
\(x^2 + 5x ~~~~~~~~~~=~~24\)

The complete the square step is to add the square of half of the x-term coefficient.
The x-term coefficient is 5. Half of 5 is \(\dfrac{5}{2} \). The square of \(\dfrac{5}{2} \) is \(\dfrac{25}{4} \). We add \(\dfrac{25}{4} \) to both sides to complete the square.

Answer 8

\(x^2 + 5x + \dfrac{25}{4} = 24 + \dfrac{25}{4} \)

\(x^2 + 5x + \dfrac{25}{4} = \dfrac{96}{4} + \dfrac{25}{4} \)

\(x^2 + 5x + \dfrac{25}{4} = \dfrac{121}{4}\)

\(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4} \)

We have finished the step of completing the square. Now we take the square root of both sides.

Answer 9

Step 2. Take square root of both sides.

Rule: If \(x^2 = k\), where \(k\) is a number, then \(x = \pm k\).

Because of the rule above, we must be careful to include both the positive and negative roots of the number on the right side of the equal sign.

Answer 10

\(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4}\)

\( x + \dfrac{5}{2} = \pm\sqrt{\dfrac{121}{4}}\)

Notice the \(\pm\) sign on the right side.

Step 3. Separate the equations and solve for x.

\( x + \dfrac{5}{2} = \pm \dfrac{11}{2}\)

Now we separate the above into two equations, one for the positive root, and one for the negative root.

\(x + \dfrac{5}{2} = \dfrac{11}{2}\) or \(x + \dfrac{5}{2} = -\dfrac{11}{2}\)

\(x = \dfrac{6}{2}\) or \(x = -\dfrac{16}{2}\)

\(x = 3\) or \(x = -8\)

The solutions to the quadratic equation are 3 and -8.
When we add the solutions, we get:

\(3 + (-8) = -5\)