Question

solve the equation using the square root property.

\\5(x + 1)^2 - 1 = 34\\

the solution set is \\{\quad\\}.
(simplify your answer. type exact answers, using radicals as needed.)

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Isolate the squared term

Add \( 1 \) to both sides of the equation:

$$ 5(x + 1)^2 = 35 $$

Divide both sides by \( 5 \):

$$ (x + 1)^2 = 7 $$

Step 2: Apply the square root property

Take the square root of both sides, remembering to include both positive and negative roots:

$$ x + 1 = \pm\sqrt{7} $$

Step 3: Solve for x

Subtract \( 1 \) from both sides to isolate \( x \):

$$ x = -1 \pm \sqrt{7} $$

Answer:

\( -1 + \sqrt{7}, -1 - \sqrt{7} \)