Final answer:
To solve the equation (2x-5)(x+4) = 3x + 30, we expanded and simplified it to form a quadratic equation, 2x^2 + 3x - 50 = 0. Factoring the quadratic gave us two potential solutions, x = 5 and x = -5, but we disregard the negative solution in context, leaving x = 5 as the final answer.
Step-by-step explanation:
Given the equation (2x-5)(x+4) = 3x + 30, we need to find the value of x. To solve for x, we first expand the left side of the equation:
2x2 + 8x - 5x - 20 = 3x + 30
This simplifies to:
2x2 + 3x - 20 - 3x = 30
Now, we have a quadratic equation of the form ax2 + bx + c = 0:
2x2 = 30 + 20
2x2 - 50 = 0
To find x, we can factor the quadratic equation or use the quadratic formula, x = (-b ± √(b2 - 4ac)) / (2a). However, in this case, factoring will suffice. Thus:
(x - 5)(2x + 10) = 0
Setting each factor equal to zero gives us two possible solutions for x:
- x - 5 = 0, which gives x = 5
- 2x + 10 = 0, which gives x = -5.
However, since a negative distance does not make sense in this context, we can disregard the negative solution. Therefore, the solution for x is 5.