Algebra anyone?

Question

Let the function f be defined by f(x) = x2 - 7x + 10 and f(t + 1) = 15, what is one possible value of t?

What will happen now?

Answer 1

f(x) = x^2 - 7x + 10

f(t + 1) = 15
Also, f(t + 1) = (t + 1)^2 - 7(t + 1) + 10

So,
(t + 1)^2 - 7(t + 1) + 10 = 15
t^2 + 2t + 1 - 7t - 7 = 5
t^2 - 5t - 6 = 5
t^2 - 5t - 11 = 0

Use the quadratic formula:

t = [5 +/- sqrt(25 + 44)]/2
t = [5 +/- sqrt 69]/2

The possible values of t are:

t = (5 + sqrt 69)/2
and
t = (5 - sqrt 69)/2

Answer 2

f(t + 1) = 15
(t + 1)² - 7(t + 1) + 10 = 15
t² + 2t + 1 - 7t - 7 - 5 = 0
t² - 5t - 11 = 0
t = [ 5 ± √(25 + 44)] / 2
t = [5 ± √69 ] / 2
t = 6.65

Answer 3

substitute x = (t+1)

(t+1)^2 - 7(t+1) + 10 = 15
(t^2 + 2t + 1) - 7(t + 1) - 5 = 0
t^2 - 5t - 5 = 0

now use your quad eq to solve for t.

t = 5 + sqrt(25 + 20) /2