Pregunta
Solve the quadratic equation. Write the smaller answer first. \( x^{2}-5 x=24 \) \( x=\square \) A \( x=\square \)
Ask by Ryan Daniels. in the United States
Feb 21,2025
Solución de inteligencia artificial de Upstudy
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\( x=-3 \) and \( x=8 \).
Solución
Solve the equation \( x^{2}-5x=24 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(x^{2}-5x=24\)
- step1: Move the expression to the left side:
\(x^{2}-5x-24=0\)
- step2: Factor the expression:
\(\left(x-8\right)\left(x+3\right)=0\)
- step3: Separate into possible cases:
\(\begin{align}&x-8=0\\&x+3=0\end{align}\)
- step4: Solve the equation:
\(\begin{align}&x=8\\&x=-3\end{align}\)
- step5: Rewrite:
\(x_{1}=-3,x_{2}=8\)
The solutions to the quadratic equation \(x^{2}-5x=24\) are \(x=-3\) and \(x=8\).
Therefore, the smaller answer is \(x=-3\) and the larger answer is \(x=8\).
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Simplifique esta solución Beyond the Answer
First, let's rearrange the equation \( x^{2}-5 x-24=0 \) to standard form. Now, we can use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2-4ac}}{2a} \), where \( a=1 \), \( b=-5 \), and \( c=-24 \). Plugging in the values, we find: 1. Calculate the discriminant: \( b^2 - 4ac = (-5)^2 - 4(1)(-24) = 25 + 96 = 121 \). 2. Now, the square root of the discriminant is \( \sqrt{121} = 11 \). 3. Plugging everything into the formula gives: \( x = \frac{5 \pm 11}{2} \). This leads to two solutions: - \( x = \frac{16}{2} = 8 \) - \( x = \frac{-6}{2} = -3 \) Thus, \( x=-3 \) A \( x=8 \).
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