Question 41
Solve the equation. Simplify all irrational solutions.
5x^2 + 14x = x + 6
x= { -3, 2/5}
x = { -3,5}
x = { 15, 5}
x= {2/3,3}
To solve the equation 5x^2 + 14x = x + 6, we first need to rearrange it to form a quadratic equation set to zero.
5x^2 + 14x - x - 6 = 0
5x^2 + 13x - 6 = 0
Next, we can factor this quadratic equation by finding two numbers that multiply to get -30 (product of 5 and -6) and add up to 13. Those numbers are 15 and -2.
So, the factored form of the quadratic equation is:
5x^2 + 15x - 2x - 6 = 0
5x(x + 3) - 2(x + 3) = 0
(5x - 2)(x + 3) = 0
Setting each factor to zero gives us the possible solutions:
5x - 2 = 0 or x + 3 = 0
5x = 2 or x = -3
x = 2/5 or x = -3
Therefore, the solutions are x = -3 and x = 2/5.