Question

solve the following equation:
$x^2 = 13x - 12$
set the equation equal to zero with quadratic term positive:

factors to:

$x = $

Explanation:

Step1: Rearrange to standard form

To set the equation \( x^{2}=13x - 12 \) equal to zero with the quadratic term positive, we subtract \( 13x \) and add \( 12 \) to both sides.
\( x^{2}-13x + 12=0 \)

Step2: Factor the quadratic

We need to find two numbers that multiply to \( 12 \) and add up to \( - 13 \). The numbers are \( -1\) and \( - 12 \). So we can factor the quadratic as:
\( (x - 1)(x - 12)=0 \)

Step3: Solve for \( x \)

Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).
If \( x-1=0 \), then \( x = 1 \).
If \( x - 12=0 \), then \( x=12 \).

Answer:

Set the equation equal to zero with quadratic term positive: \( \boldsymbol{x^{2}-13x + 12 = 0} \)

Factors to: \( \boldsymbol{(x - 1)(x - 12)=0} \)

\( x=\boldsymbol{1} \) or \( \boldsymbol{x = 12} \)