Ask a New Question
Menu

Question

Solve the following quadratic equation using square roots: −9+(x−3)2−4=−4
−
9
+
(
𝑥
−
3
)
2
−
4
=
−
4
(1 point)
Responses

{2, -8}
{2, -8}

{8, -2}
{8, -2}

{28, -22}
{28, -22}

{16, -10}

1 answer

To solve the equation \( -9 + (x - 3)^2 - 4 = -4 \), we can start by simplifying the equation.

  1. First, we can combine the constants on the left side: \[ -9 - 4 + (x - 3)^2 = -4 \] This simplifies to: \[ -13 + (x - 3)^2 = -4 \]

  2. Next, we can add 13 to both sides: \[ (x - 3)^2 = -4 + 13 \] Which simplifies to: \[ (x - 3)^2 = 9 \]

  3. Now, we take the square root of both sides: \[ x - 3 = \pm 3 \]

  4. This gives us two separate equations:

    1. \( x - 3 = 3 \)
    2. \( x - 3 = -3 \)

  5. Solving these equations:

    • For \( x - 3 = 3 \): \[ x = 3 + 3 = 6 \]
    • For \( x - 3 = -3 \): \[ x = 3 - 3 = 0 \]

Thus, the solutions are \( x = 6 \) and \( x = 0 \).

Now, let's match these solutions to the available options: None of the provided responses in your question match \( {6, 0} \).

If you'd like to clarify or present different options, please do!