Question 41
Solve the equation. Simplify all irrational solutions.
5x^2+14x=x+6
a. x={-3,2/5}
b. x={-3,5}
c. x={15,5}
d. x={2/3,3}
To solve the equation, we first need to move all terms to one side to set the equation equal to 0.
5x^2 + 14x - x - 6 = 0
This simplifies to:
5x^2 + 13x - 6 = 0
Now, we can factor or use the quadratic formula to solve for x. Factoring may not be easy in this case, so we will use the quadratic formula:
x = [-b ± √(b^2 - 4ac)] / 2a
Plugging in the values from our equation:
x = [-13 ± √(13^2 - 4(5)(-6))] / 2(5)
x = [-13 ± √(169 + 120)] / 10
x = [-13 ± √289] / 10
x = [-13 ± 17] / 10
This gives us two possible solutions:
x = (4/10) or x = (-30/10)
Simplifying these solutions, we get:
x = 2/5 or x = -3
Therefore, the correct answer is:
a. x={-3,2/5}