Question
Solve the following equation by the square root method. \[ (4 y+6)^{2}=36 \] Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \{\square\} \). (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) B. There nolution.
Ask by Graham Murphy. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solution set is \(\{-3, 0\}\).
Solution
Solve the equation \( (4y+6)^2=36 \).
Solve the quadratic equation by following steps:
- step0: Solve using square roots:
\(\left(4y+6\right)^{2}=36\)
- step1: Simplify the expression:
\(4y+6=\pm \sqrt{36}\)
- step2: Simplify the expression:
\(4y+6=\pm 6\)
- step3: Separate into possible cases:
\(\begin{align}&4y+6=6\\&4y+6=-6\end{align}\)
- step4: Solve the equation:
\(\begin{align}&y=0\\&y=-3\end{align}\)
- step5: Rewrite:
\(y_{1}=-3,y_{2}=0\)
The solutions to the equation \((4y+6)^2=36\) are \(y=-3\) and \(y=0\).
Therefore, the correct choice is:
A. The solution set is \(\{-3, 0\}\).
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Simplify this solution The Deep Dive
To solve the equation \((4y + 6)^{2} = 36\) using the square root method, we start by taking the square root of both sides: \[ 4y + 6 = \pm 6 \] This gives us two separate equations to solve: 1. \(4y + 6 = 6\) 2. \(4y + 6 = -6\) **For the first equation**: \[ 4y + 6 = 6 \\ 4y = 6 - 6 \\ 4y = 0 \\ y = 0 \] **For the second equation**: \[ 4y + 6 = -6 \\ 4y = -6 - 6 \\ 4y = -12 \\ y = -3 \] Thus, the solution set is \(\{0, -3\}\). A. The solution set is \(\{0, -3\}\).
