Question

4 q squared plus 3 q equals 3 q squared minus 4 q plus 18

Answer 1

To solve this equation, we first need to simplify both sides by combining like terms:

4q^2 + 3q = 3q^2 - 4q + 18

Subtract 3q from both sides:

4q^2 + 3q - 3q = 3q^2 - 4q - 3q + 18

Which simplifies to:

4q^2 = 3q^2 - 7q + 18

Next, subtract 3q^2 from both sides:

4q^2 - 3q^2 = 3q^2 - 3q^2 - 7q + 18

Which simplifies to:

q^2 = -7q + 18

Now, move all terms to one side of the equation:

q^2 + 7q - 18 = 0

This is a quadratic equation that can be factored:

(q + 9)(q - 2) = 0

By setting each factor equal to zero, we get two possible solutions:

q + 9 = 0
q = -9

q - 2 = 0
q = 2

So, the solutions to the equation are q = -9 or q = 2.