Problem: (x+9)(x-5) = -13
(x + 9)(x - 5) = -13
x^2 - 5x + 9x - 45 = -13
x^2 + 4x - 45 = -13
x^2 + 4x - 45 + 13 = -13 + 13
x^2 + 4x - 32 = 0
Now, we can work on getting the values for x.
-b ± sqrt(b^2 - 4*a*c)
x = -----------------------------
2a
-4 ± sqrt(4^2 - 4*1*(-32))
x = ----------------------------------
2(1)
-4 ± sqrt(16 - (-128))
x = ------------------------------
2
-4 ± sqrt(16 + 128)
x = --------------------------
2
-4 ± sqrt(144)
x = --------------------
2
-4 ± 12
x = ------------
2
-4 + 12 -4 - 12
x = ------------- and x = -------------
2 2
8 -16
x = ----- and x = --------
2 2
x = 4 and x = -8
Always verify your work.
(x + 9)(x - 5) = -13
(4 + 9)(4 - 5) = -13
(13)(-1) = -13
-13 = -13
(x + 9)(x - 5) = -13
(-8 + 9)(-8 - 5) = -13
(1)(-13) = -13
-13 = -13
Answer: x = 4 and x = -8