Question

Solve the quadratic equation 5x² −20x−60=5.?

A) x=3 or x=−4
B) x=4 or x=−3
C) x=5 or x=−6
D) x=6 or x=−5

Answer 1

The quadratic equation 5x² −20x−60=5 is first simplified to 5x² −20x−65=0, and then factored to (x−3)(x+4)=0. This leads to the solutions x=3 or x=−4.

Step-by-step explanation:

To solve the quadratic equation 5x² −20x−60=5, we first need to bring the equation to the standard form ax²+bx+c=0. Subtracting 5 from both sides, we get 5x² −20x−60−5=0 which simplifies to 5x² −20x−65=0. We can then factor out a 5, leading to x² −4x−13=0.

Now, we look for two numbers that multiply to −13 and add up to −4. These numbers are 3 and −7. Therefore, we can factor the quadratic as (x−3)(x+4)=0. Setting each factor equal to zero gives us the solutions x=3 and x=−4. Thus, the correct answer is x=3 or x=−4.

The quadratic equation 5x² −20x−60=5 is first simplified to 5x² −20x−65=0, and then factored to (x−3)(x+4)=0. This leads to the solutions x=3 or x=−4.