Question

1. $4q^2 + 3q = 3q^2 - 4q + 18$

Explanation:

Step1: Move all terms to left side

Subtract \(3q^2\), add \(4q\), and subtract \(18\) from both sides:
\(4q^2 + 3q - 3q^2 + 4q - 18 = 0\)
Simplify like terms:
\(q^2 + 7q - 18 = 0\)

Step2: Factor the quadratic equation

Find two numbers that multiply to \(-18\) and add to \(7\). The numbers are \(9\) and \(-2\).
So, \(q^2 + 7q - 18=(q + 9)(q - 2)=0\)

Step3: Solve for q

Set each factor equal to zero:
\(q + 9 = 0\) or \(q - 2 = 0\)
For \(q + 9 = 0\), \(q=-9\); for \(q - 2 = 0\), \(q = 2\)

Answer:

\(q = -9\) or \(q = 2\)