Question
c) \( x^{2}-2 x-8=0 \)
Ask by Mann Salazar. in South Africa
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \(x=-2\) and \(x=4\).
Solution
Solve the equation \( x^{2}-2x-8=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-2x-8=0\)
- step1: Factor the expression:
\(\left(x-4\right)\left(x+2\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-4=0\\&x+2=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=4\\&x=-2\end{align}\)
- step4: Rewrite:
\(x_{1}=-2,x_{2}=4\)
The solutions to the equation \(x^{2}-2x-8=0\) are \(x=-2\) and \(x=4\).
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Simplify this solution The Deep Dive
Did you know that this quadratic equation can be solved using the quadratic formula? You simply plug the coefficients \(a = 1\), \(b = -2\), and \(c = -8\) into the formula \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\). By doing the calculations, you’ll find two solutions, which gives you the values of \(x\) where the equation holds true! Here’s a quick tip: always double-check your signs and calculations when using the formula. Common mistakes include miscalculating the discriminant or flipping the sign on \(b\). A fun way to avoid this is to write out each step, like a recipe, so you can catch any ‘oopsies’ before reaching the final solution!
