Final answer:
The student needs to solve a quadratic equation by factoring it. The equation is x squared plus seventeen x equals negative 72, which is factored to find the solutions x = -8 or x = -9.
Step-by-step explanation:
The student is asking to solve the quadratic equation by factoring.
The equation provided is x squared plus seventeen x equals negative 72, which can be written as x2 + 17x + 72 = 0.
To solve this, one would typically try to find two numbers that multiply to give the constant term (72) and add to give the coefficient of the x term (17).
First, we would rewrite the equation in the standard quadratic form: x2 + 17x + 72 = 0.
Then, we find factors of the constant term: (x + 8)(x + 9) = 0.
Next, we set each factor equal to zero and solve for x: x + 8 = 0 or x + 9 = 0.
This gives us the solutions x = -8 or x = -9.
Since this problem specifically asks for factoring, we avoid using the quadratic formula, which is another method of solving quadratic equations.