Question

Using the factoring​ method, solve for the roots of the quadratic equation. Be sure to place your equation in standard form before factoring.x squared equals 6 x plus 27Question content area bottomPart 1xequalsenter your response here ​(Simplify your answer. Use a comma to separate answers as​ needed.)

Answer 1

To solve the quadratic equation \( x^2 = 6x + 27 \) using the factoring method, we first need to rearrange it into standard form, which is \( ax^2 + bx + c = 0 \).

1. Move all terms to one side of the equation:
\[
x^2 - 6x - 27 = 0
\]

Now we have the quadratic in standard form \( ax^2 + bx + c = 0 \), where \( a = 1 \), \( b = -6 \), and \( c = -27 \).

2. Next, we will factor the quadratic \( x^2 - 6x - 27 \). We need to find two numbers that multiply to \( -27 \) (the constant term) and add up to \( -6 \) (the coefficient of \( x \)).

The two numbers that meet these criteria are \( -9 \) and \( 3 \) because:
- \( -9 \times 3 = -27 \)
- \( -9 + 3 = -6 \)

3. We can now factor the quadratic:
\[
(x - 9)(x + 3) = 0
\]

4. To find the roots, we set each factor equal to zero:
\[
x - 9 = 0 \quad \Rightarrow \quad x = 9
\]
\[
x + 3 = 0 \quad \Rightarrow \quad x = -3
\]

5. The roots of the equation are:
\[
x = 9, -3
\]

Thus, the final answer is:
\[
\boxed{9, -3}
\]