What is the correct answer when you solve 5x = 6 − x^2?
To solve the equation 5x = 6 − x^2, you need to rearrange it to standard quadratic form (ax^2 + bx + c = 0).
Rearranging the equation, we have: x^2 + 5x - 6 = 0
To factorize the quadratic equation, we need to find two numbers that multiply to give -6 and add up to 5. The numbers are 6 and -1.
Therefore, we can factorize the equation as: (x + 6)(x - 1) = 0
Setting each factor equal to zero, we have: x + 6 = 0 and x - 1 = 0
Solving for x, we get:
x = -6
x = 1
So the correct answers are x = -6 and x = 1.