Question 41
Solve the equation. Simplify all irrational solutions.
5x^2 + 14x = x + 6
To solve the given equation, we first need to set it equal to zero:
5x^2 + 14x - x - 6 = 0
5x^2 + 13x - 6 = 0
Next, we need to factor the quadratic equation. To factor this equation, we look for two numbers that multiply to -30 (5*-6) and add up to 13.
The numbers are 15 and -2.
5x^2 + 15x - 2x - 6 = 0
5x(x + 3) - 2(x + 3) = 0
(5x - 2)(x + 3) = 0
So, the solutions are:
5x - 2 = 0
5x = 2
x = 2/5
x + 3 = 0
x = -3
Therefore, the solutions to the equation 5x^2 + 14x = x + 6 are x = 2/5 and x = -3.