4
QuizMultiple Choice

Solving Quadratic Equations: Completing the Square (Continued) — Quiz

Question 4 • Algebra I

Patel is solving 8 x squared plus 16 x plus 3 is equal to 0 Which steps could he use to solve the quadratic equation? Choose three correct answers.

Answer
A
8 times open paren x squared plus 2 x close paren is equal to negative 3
B
8 times open paren x squared plus 2 x plus 1 close paren is equal to 3 plus 1
C
8 times open paren x squared plus 2 x plus 1 close paren is equal to negative 3 plus 8
D
x is equal to negative 1 plus or minus square root of 5 eighths
E
x is equal to negative 1 plus or minus square root of 4 eighths

Explanation

Move 3 to the right to get 8x² + 16x = −3, then factor out 8: 8(x² + 2x) = −3, which is choice A. To complete the square, add 1 inside the parentheses; because it is multiplied by 8, this adds 8 to the left, so the right side becomes −3 + 8 = 5, as in choice C. Then (x + 1)² = 5/8, so x = −1 ± √(5/8), as stated in choice D.

AI-written and checked against the verified answer.

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