Question

$x^2 - 3x - 54 = 0$
factors to:
$x = $

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to -54 and add up to -3. The numbers are -9 and 6, since \((-9)\times6 = -54\) and \(-9 + 6 = -3\). So we can factor \(x^2 - 3x - 54\) as \((x - 9)(x + 6)\).
\[x^2 - 3x - 54=(x - 9)(x + 6)\]

Step2: Solve for \(x\)

Set each factor equal to zero:

• For \(x - 9 = 0\), we get \(x = 9\).
• For \(x + 6 = 0\), we get \(x = -6\).

Answer:

Factors to: \((x - 9)(x + 6) = 0\)
\(x = 9\) or \(x = -6\)