Final answer:
The quadratic equation 8x(x+3)=2x−5 is solved by first expanding and rearranging to form 8x² + 22x + 5 = 0. It can then be factored into (4x + 5)(2x + 1) = 0, and by using the Zero Product Property, we find the solutions x = -5/4 or x = -1/2.
Step-by-step explanation:
To solve the quadratic equation 8x(x+3)=2x−5, we first expand the left side and then rearrange to set the equation to zero:
8x² + 24x = 2x - 5
8x² + 22x + 5 = 0
Now we factor the quadratic equation if possible or alternatively, use the quadratic formula. Let's see if factoring is possible:
(4x + 5)(2x + 1) = 0
Applying the Zero Product Property, we set each factor equal to zero:
- 4x + 5 = 0 → x = -5/4
- 2x + 1 = 0 → x = -1/2
Hence, the solution to the quadratic equation is x = -5/4 or x = -1/2.