Question

M^2 = (4x + 5) and m^2 - 4 = (x^2 – 27). How to solve this?

a) x = 3
b) x = -3
c) x = 4
d) x = -4

Answer 1

To solve the given equations m^2 = (4x + 5) and m^2 - 4 = (x^2 - 27), use the substitution method and solve for x.

Step-by-step explanation:

To solve the equations m^2 = (4x + 5) and m^2 - 4 = (x^2 - 27), we can use the substitution method:

1. Start by solving the first equation for m^2:
   1. m^2 = 4x + 5
2. Substitute this equation into the second equation:
   1. (4x + 5) - 4 = (x^2 - 27)
3. Simplify:
   1. 4x + 1 = x^2 - 27
4. Rearrange the equation to get it in quadratic form:
   1. x^2 - 4x - 28 = 0
5. Factor the quadratic equation:
   1. (x - 7)(x + 4) = 0
6. Set each factor equal to zero and solve for x:
   1. x - 7 = 0 -> x = 7
   2. x + 4 = 0 -> x = -4