Question
Solve the quadratic equation by using the square root property. (Enter your answers as a comma-separated list.) \[ (x-5)^{2}=7 \] \( x=\square \)
Ask by Ortega Chang. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 5 + \sqrt{7},\ 5 - \sqrt{7} \)
Solution
1. Start with the equation:
\[
(x-5)^2 = 7
\]
2. Apply the square root property:
\[
x-5 = \pm\sqrt{7}
\]
3. Solve for \( x \) by adding \( 5 \) to both sides:
\[
x = 5 \pm \sqrt{7}
\]
4. The solutions are:
\[
x = 5+\sqrt{7},\ 5-\sqrt{7}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To solve the quadratic equation \((x-5)^{2}=7\), we start by applying the square root property. First, take the square root of both sides: \[ x - 5 = \pm \sqrt{7} \] Now, isolate \(x\) by adding 5 to both sides: \[ x = 5 \pm \sqrt{7} \] This gives us two solutions: \[ x = 5 + \sqrt{7}, \, x = 5 - \sqrt{7} \] So, the final answers are: \( x = 5 + \sqrt{7}, 5 - \sqrt{7} \)
