Solve the equation 5x^2 + 14x = x + 6. Simplify ALL IRRATIONAL SOLUTIONS. Select the correct answers that apply from the following:
a) x = {-3, 2/5}
b) x = {-3,5}
c) x = {15, 5}
d) x = {2/3, 3}
To solve the equation 5x^2 + 14x = x + 6, we must first move all terms to one side to set the equation to zero:
5x^2 + 14x - x - 6 = 0
5x^2 + 13x - 6 = 0
Next, we need to factor the quadratic equation:
5x^2 + 13x - 6 = (5x - 2)(x + 3) = 0
Setting each factor to zero gives us the possible solutions:
5x - 2 = 0
5x = 2
x = 2/5
and
x + 3 = 0
x = -3
Therefore, the solutions are x = {-3, 2/5}. So the correct answer is a) x = {-3, 2/5}.