Question
Use factoring to solve the quadratic equation. \[ x^{2}-2 x-15=0 \]
Ask by Carrillo Morgan. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The solutions are \(x=-3\) and \(x=5\).
Solution
Solve the equation \( x^{2}-2x-15=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-2x-15=0\)
- step1: Factor the expression:
\(\left(x-5\right)\left(x+3\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-5=0\\&x+3=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=5\\&x=-3\end{align}\)
- step4: Rewrite:
\(x_{1}=-3,x_{2}=5\)
The solutions to the quadratic equation \(x^{2}-2x-15=0\) are \(x=-3\) and \(x=5\).
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Simplify this solution Beyond the Answer
To factor the quadratic equation \( x^{2}-2 x-15=0 \), we look for two numbers that multiply to \(-15\) (the constant term) and add up to \(-2\) (the coefficient of the linear term). The numbers \(-5\) and \(3\) fit this criterion since \((-5) \times 3 = -15\) and \((-5) + 3 = -2\). Now we can rewrite the equation as: \[ (x - 5)(x + 3) = 0 \] Next, we set each factor equal to zero: 1. \( x - 5 = 0 \) → \( x = 5 \) 2. \( x + 3 = 0 \) → \( x = -3 \) Thus, the solutions to the equation are \( x = 5 \) and \( x = -3 \). Now you have found the roots using factoring in a fun and engaging way!
