solve the equatoion

Question

4(x+1)^2=100.

Answer 1

The equation is 4(x + 1)^2 = 100.

Apply formula : (a + b )^2 = a ^2 + 2ab + b ^2.

4(x ^2 + 2x + 1) = 100

Divide each side by 4.

x ^2 + 2x + 1 = 100/4

x ^2 + 2x + 1 = 25

Subtract 25 from each side.

x ^2 + 2x + 1 - 25 = 0

x ^2 + 2x - 24= 0

x ^2 + 6x - 4x - 24= 0

Factor : (x + 6)(x - 4) = 0.

Apply zero product property.

(x + 6) = 0 (or) (x - 4) = 0

x = 4 (or) - 6.

Solution is x = 4 (or) - 6.