Question
upstudy study bank question image url

Quadratic equations 1 Solve \( x^{2}-x-30=0 \) using the factorisation method. \( x^{2}-x-30=0 \) \( x^{2}+\square x-\square x-30=0 \) \( (x+\square)(x-\square)=0 \) \( x+\square-0 \) or \( x-\square= \) \( x=-\square \) or \( x=\square \)

Ask by Knight Greene. in Nigeria
Jan 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The solutions are \(x=-5\) and \(x=6\).

Solution

Solve the equation \( x^{2}-x-30=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(x^{2}-x-30=0\) - step1: Factor the expression: \(\left(x-6\right)\left(x+5\right)=0\) - step2: Separate into possible cases: \(\begin{align}&x-6=0\\&x+5=0\end{align}\) - step3: Solve the equation: \(\begin{align}&x=6\\&x=-5\end{align}\) - step4: Rewrite: \(x_{1}=-5,x_{2}=6\) The solutions to the quadratic equation \(x^{2}-x-30=0\) using the factorization method are \(x=-5\) and \(x=6\).

Answered by UpStudy AI and reviewed by a Professional Tutor

error msg
Explain
Simplify this solution

Beyond the Answer

Let's tackle that quadratic equation! We need two numbers that multiply to -30 and add up to -1. Those numbers are -6 and 5, so we rewrite the equation as \( (x - 6)(x + 5) = 0 \). Now we set each factor equal to zero: \( x - 6 = 0 \) or \( x + 5 = 0 \). This gives us the solutions \( x = 6 \) or \( x = -5 \). And voilà, you've solved it! Now, this method of factorizing is a great time-saver! It's like being a mental ninja—quickly slicing through numbers! But remember, if the equation doesn't factor neatly, you might want to use the quadratic formula instead—keep that tool in your toolkit! Happy solving!

Related Questions

Latest Algebra Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy