Question

Write the following equation in standard form. Then solve.5 q squared minus 3 qequals4 q squared minus 5 q plus 15Question content area bottomPart 1The equation in standard form isenter your response here.

Answer 1

To rewrite the equation \( 5q^2 - 3q = 4q^2 - 5q + 15 \) in standard form, we need to move all terms to one side of the equation.

1. **Start with the given equation**:
\[
5q^2 - 3q = 4q^2 - 5q + 15
\]

2. **Subtract \( 4q^2 \), add \( 5q \), and subtract \( 15 \) from both sides**:
\[
5q^2 - 4q^2 - 3q + 5q - 15 = 0
\]

3. **Combine like terms**:
\[
(5q^2 - 4q^2) + (-3q + 5q) - 15 = 0
\]
\[
q^2 + 2q - 15 = 0
\]

So, the equation in standard form is:
\[
q^2 + 2q - 15 = 0
\]

Now, let's solve the equation using factorization or the quadratic formula.

### Factorization
1. **Find factors of -15 that add up to 2**:
The factors of -15 that work are 5 and -3.

2. **Rewrite the quadratic**:
\[
(q + 5)(q - 3) = 0
\]

3. **Set each factor to zero**:
\[
q + 5 = 0 \quad \Rightarrow \quad q = -5
\]
\[
q - 3 = 0 \quad \Rightarrow \quad q = 3
\]

### Solutions
The solutions to the equation \( q^2 + 2q - 15 = 0 \) are:
\[
q = -5 \quad \text{and} \quad q = 3
\]

Thus, you have completed both parts: the equation in standard form is \( q^2 + 2q - 15 = 0 \) and the solutions are \( q = -5 \) and \( q = 3 \).