(y-3)(y+4) = 8

Question

system of equations

Answer 1

(y-3)(y+4) = 8
system of equations

(y - 3)(y + 4) = 8
y^2 - 3y + 4y - 12 = 8
y^2 + y - 12 = 8
y^2 + y = 20

Use "completing the square."

y^2 + y + (1/2)^2 = 20 + (1/2)^2     add the square of one-half the y co-efficient
(y + 1/2)(y + 1/2) = 20.25

y + 1/2 = ± √20.25
y + 1/2 = ± 4.5

y = 4.5 - 1/2        and   y = -4.5 - 1/2
y = 4                   and   y = -5

Check both values in the original equation.

(y - 3)(y + 4) = 8
(4 - 3)(4 + 4) = 8
(1)(8) = 8
8 = 8

(y - 3)(y + 4) = 8
(-5 - 3)(-5 + 4) = 8
(-8)(-1) = 8
8 = 8

y = 4 and y = -5