anonymous
  • anonymous
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.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
alekos
  • alekos
Are you attempting to solve for x using the complete the square method?
anonymous
  • anonymous
I'm trying to get the sum of 2 solutions of the equation \[X^{2}+5x-24=0\]
alekos
  • alekos
you mean the product of two solutions, in other words you want to factorise the quadratic

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

alekos
  • alekos
(x+a)(x+b) = x^2 +5x -24
mathstudent55
  • mathstudent55
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.
alekos
  • alekos
Hmm. I don't get -5 as one of the solutions?
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
\(x^2 + 5x + \dfrac{25}{4} = 24 + \dfrac{25}{4} \) \(x^2 + 5x + \dfrac{25}{4} = \dfrac{96}{4} + \dfrac{25}{4} \) \(x^2 + 5x + \dfrac{25}{4} = \dfrac{121}{4}\) \(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4} \) We have finished the step of completing the square. Now we take the square root of both sides.
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
\(\left( x + \dfrac{5}{2} \right)^2 = \dfrac{121}{4}\) \( x + \dfrac{5}{2} = \pm\sqrt{\dfrac{121}{4}}\) 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: \(3 + (-8) = -5\)

Looking for something else?

Not the answer you are looking for? Search for more explanations.