t^2 - 10t + 24 = 0

t^2 - 10t = -24

Take half of the coefficient of t and square it.

-10t `=>` -10 `=>` -5 `=>` 25

Add this number to both sides.

t^2 - 10t + 25 = -24 + 25

t^2 - 10t + 25 = 1

Factor the polynomial using the Perfect Square Pattern.

(t - 5)^2 = 1

Square root both sides.

t - 5  = `+-` 1

t = 6

t = 4

You can check this by graphing and finding the x-intercepts.

Notice that the x-intercepts of the parabola are 4 and 6.

See the attached email for more examples of completing the square.

First, we move the 24 to the other side:

t^2 - 10t + 24 = 0

This is in standard form:  Ax^2 + Bx + C = 0, where A = 1, B = 10, and C = 24.

Subtract 24 from both sides.

t^2 - 10t = -24

Now we find half of B and square it.  That is what we add to both sides.  Half of -10 is -5 and (-5)^2 is 25.  So we will add 25 to both sides:

t^2 - 10t +25 = -24 + 25

Now we factor the first side.

(t-5)(t - 5) = 1

(t - 5)^2 = 1

t - 5 = 1 or t - 5 = -1

t = 6 or t = 4

The solution set is t = {-4, 6}.