Question

question 10 of 10
which of the following are solutions to the equation below?
check all that apply.
$(5x + 1)^2 = 7$

a. $x = \frac{\sqrt{7} - 1}{5}$
b. $x = -\frac{\sqrt{6}}{5}$
c. $x = \frac{-\sqrt{7}}{5} - 1$
d. $x = \frac{\sqrt{7}}{5} - 1$
e. $x = \frac{\sqrt{6}}{5}$
f. $x = \frac{-\sqrt{7} - 1}{5}$

Explanation:

Step1: Take square root of both sides

To solve \((5x + 1)^2 = 7\), we first take the square root of both sides. Remember that if \(y^2 = a\) (\(a\geq0\)), then \(y=\pm\sqrt{a}\). So, applying this to our equation, we get:
\(5x + 1=\pm\sqrt{7}\)

Step2: Solve for \(x\) when \(5x + 1=\sqrt{7}\)

Subtract 1 from both sides:
\(5x=\sqrt{7}-1\)
Then divide both sides by 5:
\(x = \frac{\sqrt{7}-1}{5}\)

Step3: Solve for \(x\) when \(5x + 1=-\sqrt{7}\)

Subtract 1 from both sides:
\(5x=-\sqrt{7}-1\)
Then divide both sides by 5:
\(x=\frac{-\sqrt{7}-1}{5}\)

Answer:

A. \(x = \frac{\sqrt{7}-1}{5}\), F. \(x=\frac{-\sqrt{7}-1}{5}\)