Pregunta
Solve the equation. (Enter your answers as \( a^{2}+15 a+54=0 \) SUBMIT ANSWER 12. [-/1 Points] DETAILS MOINTS MY NO Solve the equation. (Enter your answers
Ask by O'Quinn Sanders. in the United States
Feb 21,2025
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The solutions are \(a = -9\) and \(a = -6\).
Solución
Solve the equation \( a^{2}+15a+54=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(a^{2}+15a+54=0\)
- step1: Factor the expression:
\(\left(a+6\right)\left(a+9\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&a+6=0\\&a+9=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&a=-6\\&a=-9\end{align}\)
- step4: Rewrite:
\(a_{1}=-9,a_{2}=-6\)
The solutions to the equation \(a^{2}+15a+54=0\) are \(a=-9\) and \(a=-6\).
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To solve the quadratic equation \( a^{2}+15a+54=0 \), we can use the quadratic formula: \[ a = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] Here, \( a = 1 \), \( b = 15 \), and \( c = 54 \). Plugging in these values gives: \[ a = \frac{-15 \pm \sqrt{15^2 - 4(1)(54)}}{2(1)} = \frac{-15 \pm \sqrt{225 - 216}}{2} \] \[ = \frac{-15 \pm \sqrt{9}}{2} = \frac{-15 \pm 3}{2} \] This results in two possible solutions: 1. \( a = \frac{-15 + 3}{2} = \frac{-12}{2} = -6 \) 2. \( a = \frac{-15 - 3}{2} = \frac{-18}{2} = -9 \) So the solutions to the equation are \( a = -6 \) and \( a = -9 \).
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