Question
Solving Simple Quadratic Equations Quick Check
5 of 55 of 5 Items
Question
Solve the following quadratic equation using square roots: (x+36)^2−38=251.(1 point)
Responses
{253,−325}
left brace 253 comma negative 325 right brace
{17.84,−13.84}
left brace 17.84 comma negative 13.84 right brace
{−19,−53}
left brace negative 19 comma negative 53 right brace
{53,19}
Answers
GPT-4o mini
To solve the quadratic equation \((x + 36)^2 - 38 = 251\), follow these steps:
1. **Isolate the squared term**:
\[
(x + 36)^2 - 38 = 251
\]
Add 38 to both sides:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]
2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]
Since \(\sqrt{289} = 17\), we have:
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]
3. **Solve for \(x\)**:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]
- For \(x + 36 = -17\):
\[
x = -17 - 36 = -53
\]
4. **Final solutions**:
The solutions to the equation are:
\[
x = -19 \quad \text{and} \quad x = -53
\]
Thus, the correct response is:
\(\{−19,−53\}\).
1. **Isolate the squared term**:
\[
(x + 36)^2 - 38 = 251
\]
Add 38 to both sides:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]
2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]
Since \(\sqrt{289} = 17\), we have:
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]
3. **Solve for \(x\)**:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]
- For \(x + 36 = -17\):
\[
x = -17 - 36 = -53
\]
4. **Final solutions**:
The solutions to the equation are:
\[
x = -19 \quad \text{and} \quad x = -53
\]
Thus, the correct response is:
\(\{−19,−53\}\).