4(x+1)^2=100
4(x^2 + 2x + 1) = 100
x^2 + 2x + 1 = 25
x^2 + 2x - 24 = 0
-b ± √(b² - 4*a*c)
x = --------------------
2a
-2 ± √(2² - 4*1*(-24))
x = --------------------------
2(1)
-2 ± √(4 + 96)
x = ------------------
2
-2 ± √(100)
x = ------------------
2
-2 ± 10
x = ---------
2
8 -12
x = -- x = -----
2 2
x = 4 x = -6
Check the answers.
4(x^2 + 2x + 1) = 100
4(4^2 + 2(4) + 1) = 100
4(16 + 8 + 1) = 100
4(25) = 100
100 = 100 correct
4(x^2 + 2x + 1) = 100
4((-6)^2 + 2(-6) + 1) = 100
4(36 -12 + 1) = 100
4(25) = 100
100 = 100 also correct
We have x = 4 and x = -6