To solve , we first need to move all the terms to one side to write the equation in standard form. Subtracting 310 on both sides then gives .
To factor a quadratic of the form , you need to find two numbers, m and n, such that and . You can then rewrite the middle term as bx=mx+nx and factor by grouping.
For , a=3, b=−1, and so and . Therefore and since and . You can then rewrite the middle term as and then factor by grouping:
Rewrite the middle term.
Group each pair of terms.
Factor out the GCF of each pair.
Factor out .
Now that we have the equation factored, we can use the Zero Product Property to solve for x. The Zero Product Property states that if , then or . Therefore, if , then . Solving each of these for x gives:
The solutions of the equation are then and