Question
Solve the equation. Express numbers in exact simplest form. \( 3 q(q+7)=-36 \)
Ask by Huang Fowler. in the United States
Nov 13,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \(q=-4\) and \(q=-3\).
Solution
Solve the equation \( 3q(q+7)=-36 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(3q\left(q+7\right)=-36\)
- step1: Expand the expression:
\(3q^{2}+21q=-36\)
- step2: Move the expression to the left side:
\(3q^{2}+21q+36=0\)
- step3: Factor the expression:
\(3\left(q+3\right)\left(q+4\right)=0\)
- step4: Divide the terms:
\(\left(q+3\right)\left(q+4\right)=0\)
- step5: Separate into possible cases:
\(\begin{align}&q+3=0\\&q+4=0\end{align}\)
- step6: Solve the equation:
\(\begin{align}&q=-3\\&q=-4\end{align}\)
- step7: Rewrite:
\(q_{1}=-4,q_{2}=-3\)
The solutions to the equation \(3q(q+7)=-36\) are \(q=-4\) and \(q=-3\).
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Simplify this solution The Deep Dive
To solve the equation \( 3 q(q+7)=-36 \), first divide both sides by 3: \[ q(q+7) = -12 \] Next, rearrange it into standard quadratic form: \[ q^2 + 7q + 12 = 0 \] Now, factor the quadratic equation: \[ (q + 3)(q + 4) = 0 \] Setting each factor equal to zero gives: \[ q + 3 = 0 \quad \text{or} \quad q + 4 = 0 \] This leads to the solutions: \[ q = -3 \quad \text{or} \quad q = -4 \] So, the exact simplest form of the solutions are \( q = -3 \) and \( q = -4 \).
