Question
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 Little Haynes. 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 \(x=6\).
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Simplify this solution Mind Expander
To solve the quadratic equation \( x^{2}-x-30=0 \) using the factorisation method, we first need to find two numbers that multiply to \(-30\) (the constant term) and add up to \(-1\) (the coefficient of \(x\)). Those numbers are \(5\) and \(-6\). This allows us to rewrite the equation as \( x^{2}-6x+5x-30=0 \), which can be factored as \( (x-6)(x+5)=0 \). Setting each factor to zero gives us the solutions: \( x-6=0 \) or \( x+5=0 \), hence \( x=6 \) or \( x=-5 \). Now we have our values: \( x=-5 \) or \( x=6 \). Happy solving!
