Question

solve the following equation by either factoring or quadratic formula $3x^2 + 9x = 30$
$x_1 = \square$
$x_2 = \square$

Explanation:

Step1: Rewrite in standard form

Subtract 30 from both sides: $3x^2 + 9x - 30 = 0$. Divide all terms by 3: $x^2 + 3x - 10 = 0$.

Step2: Factor the quadratic

Find two numbers that multiply to -10 and add to 3: 5 and -2. So, $(x + 5)(x - 2) = 0$.

Step3: Solve for x

Set each factor to zero: $x + 5 = 0$ gives $x = -5$; $x - 2 = 0$ gives $x = 2$.

Answer:

$x_1 = 2$, $x_2 = -5$