Question

quiz instructions

for this quiz answer each question and fill in the blank (box) with the

fractional quantities can be written using the /, meaning one-half can be typed a should be exact, not rounded.

you have 20 minutes to complete the quiz.

you have only one attempt.

question 5

solve the equation. type your answer(s) in the box, separate multiple answers with a comma. answers should be exact, not rounded.

\\(x - 3)^2 + 5 = 30\\

\\x = \\{\quad\\}\\

Explanation:

⚡ Using what you learned: factoring and solving quadratic equations

Step 1: Isolate the squared term

Subtract \( 5 \) from both sides of the equation:

$$ (x - 3)^2 = 25 $$

Step 2: Take the square root of both sides

Apply the square root property:

$$ x - 3 = \pm\sqrt{25} $$

$$ x - 3 = \pm 5 $$

Step 3: Solve for \( x \)

Split the equation into two separate cases:

1. \( x - 3 = 5 \implies x = 8 \)
2. \( x - 3 = -5 \implies x = -2 \)

Answer:

-2, 8