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 \( q = 3 \).