A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Solve the equation algebraically 5rad(x+4) =absolute value (x-3)

  • This Question is Closed
  1. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[5\sqrt{x+4}=\left| x-3 \right|\]

  2. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large { 5\sqrt{x+4}=| x-3 |\\\quad\\ \implies \begin{cases} +(5\sqrt{x+4})=x-3\implies 5\sqrt{x+4}=x-3\\ 5\sqrt{x+4}+3=x \\\hline\\ -(5\sqrt{x+4})=x-3\implies -5\sqrt{x+4}=x-3\\ -5\sqrt{x+4}+3=x \end{cases} }\) two cases, for an absolute value expression, thus two values for "x" keep in mind you always have a + and - case with absolute value expressions

  3. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok i got that but I still dont know how to solve this

  4. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ohh shoot... aehmm yeah... ok... we do have an "x" on the left side... I see

  5. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    have you ... covered the factoring quadratics?

  6. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idk maybe

  7. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmmm meaning, have you factored something like \(x^2+3x-4\) yet?

  8. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah

  9. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok.. have you covered the quadratic formula yet?

  10. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yass

  11. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    k

  12. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let us pick the 1st case, one sec

  13. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\bf 5\sqrt{x+4}=x-3\impliedby \textit{let us square both sides} \\ \quad \\ (5\sqrt{x+4})^2=(x-3)^2\implies (5)^2(\sqrt{x+4})^2=x^2-6x+9 \\ \quad \\ 25(x+4)=x^2-6x+9\implies 25x+100=x^2-6x+9 \\ \quad \\ 0=x^2-31x-91\) now, we end up with a quadratic equation 91 is a prime, pretty sure of that so it won't factor nicely, so we could get the middle term of -6 so you'd need to use the quadratic formula for that

  14. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\bf 0=x^2-31x-91\qquad \qquad \textit{quadratic formula} \\ \quad \\ 0={\color{blue}{ 1}}x^2{\color{red}{ -31}}x{\color{green}{ -91}} \qquad \qquad x= \cfrac{ - {\color{red}{ b}} \pm \sqrt { {\color{red}{ b}}^2 -4{\color{blue}{ a}}{\color{green}{ c}}}}{2{\color{blue}{ a}}}\)

  15. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now let use pick the 2nd case \(\bf -5\sqrt{x+4}=x-3\impliedby \textit{let us square both sides} \\ \quad \\ (-5\sqrt{x+4})^2=(x-3)^2\implies (-5)^2(\sqrt{x+4})^2=x^2-6x+9 \\ \quad \\ 25(x+4)=x^2-6x+9\implies 25x+100=x^2-6x+9 \\ \quad \\ 0=x^2-31x-91\) notice, the -5, turns to a positive 25 and we end up with the same equation as the 1st case so, using the quadratic formula for the 1st one, solves also the 2nd one

  16. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok thank you sooooo much @jdoe0001

  17. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ywq

  18. jdoe0001
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yw rather

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.