Verified answer

You can solve it by (1) factoring (maybe), (2) quadratic formula, or (3) completing the square.

I'll use method 1 because it's easier if the expression can be factored.

(x + 8)(x - 9) = 0

x = -8, or x = 9

Take care,

David

Perhaps you should learn how to do these instead of copying your answers from here?

x² – x – 72 = 0

look for two numbers that can be multiplied together to get 72 and have a difference of 1. 8 and 9 will do.

(x - 9)(x + 8) = 0

x = 9, -8

.

This is a quadratic equation (QE). In general, the solutions (x1 and x2)

of a generic QE { ax^2 + bx + c = 0} are

x1 = [- b + sqrt(b^2 - 4ac)]/2a

and

x2 = [- b - sqrt(b^2 - 4ac)]/2a

In your example, a = 1, b = -1 and c = -72

(1) So, by substitution,

x1 = [- (-1) + sqrt((-1)^2 - 4*(1)*(-72)]/(2*1)

x1 = [1 + sqrt(289)]/2 = [1 + 17]/2 = 9

So, (x - 9) is one of the two factors of your QE.

(2) By substitution, you will find that x2 = - 8, meaning that

(x + 8) is the other QE factor so . . .

(3) x^2 - x - 72 = (x + 8)*(x - 9) = 0

PS: You may want to memorize the above-cited solutions of the generic QE.

I would love to help but if you don't know how to do it, you'll fall behind. I suggest that you talk to her and ask for some assistance. Copying other peoples homework never helps.

I can help by telling you what to do but I will not give you the answer. Factor x^2 - x - 72 = 0, once you factor use the zero product property and then check for extraneous solutions.

Good Luck!

x^2 – x – 72 = 0

(x-9)(x+8)=0

x = 9 or -8

x^2-x-72=0

(x-9)(x+8)=0

x=9 or -8

Just use the quadratic formula because the equation is of the form ax^2+bx+c =

a(x^2 + b/ax + (b/2a)^2)+c = ab^2/4a^2

a(x+b/2a)^2 = b^2/ 4a -c

= b^2/4a - 4ac/4a

= b^2 - 4ac/ 4a^2

x = (b^2 - 4ac)^1/2 / 2a -b/2a

take it from there

(x - 9) (x + 8) = 0

x = 9 , x = - 8