# how do you solve x^2-3x-18=0?

• Question Number 1 :

For this equation x^2 – 3*x – 18 = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use factorization to find the root of the equation !

C. Use completing the square to find the root of the equation !

The equation x^2 – 3*x – 18 = 0 is already in a*x^2+b*x+c=0 form.

As the value is already arranged in a*x^2+b*x+c=0 form, we get the value of a = 1, b = -3, c = -18.

1A. Find the roots using Quadratic Formula !

Remember the formula,

x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

Since a = 1, b = -3 and c = -18,

we just need to subtitute the value of a,b and c in the abc formula.

Which produce x1 = (-(-3) + sqrt( (-3)^2 – 4 * (1)*(-18)))/(2*1) and x2 = (-(-3) – sqrt( (-3)^2 – 4 * (1)*(-18)))/(2*1)

Which is the same as x1 = ( 3 + sqrt( 9+72))/(2) and x2 = ( 3 – sqrt( 9+72))/(2)

Which make x1 = ( 3 + sqrt( 81))/(2) and x2 = ( 3 – sqrt( 81))/(2)

We got x1 = ( 3 + 9 )/(2) and x2 = ( 3 – 9 )/(2)

The answers are x1 = 6 and x2 = -3

1B. Use factorization to find the root of the equation !

x^2 – 3*x – 18 = 0

( x – 6 ) * ( x + 3 ) = 0

So we got the answers as x1 = 6 and x2 = -3

1C. Use completing the square to find the root of the equation !

x^2 – 3*x – 18 = 0 ,divide both side with 1

So we get x^2 – 3*x – 18 = 0 ,

Which means that the coefficient of x is -3

We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = -3/2 = -1.5

Which means we can turn the equation into x^2 – 3*x + 2.25 – 20.25 = 0

And it is the same with ( x – 1.5 )^2 – 20.25 = 0

Which is the same with (( x – 1.5 ) – 4.5 ) * (( x – 1.5 ) + 4.5 ) = 0

And it is the same with ( x – 1.5 – 4.5 ) * ( x – 1.5 + 4.5 ) = 0

Do the addition/subtraction, and we get ( x – 6 ) * ( x + 3 ) = 0

The answers are x1 = 6 and x2 = -3

• X 2-3x-18

• Using the graph calculator: 1) Hit the Y= key, then enter next to Y1= X^2-3X-18. Hit the Graph key. You will see a graph. Now hit the 2ND and the Graph keys. You will see different values for X and Y. Since you already know the value of Y=0, you need to find the value for X, next to where the value for Y=0. Look up and down to find the + and – values of X. So, you will see that when X=6, Y1=0, likewise, when X1=-3, Y1=0. This means that the graph has a minimum and its roots are (6,0) and (-3,0).

• x^2 – 3x – 18 = 0 (factor by finding two integers that multiply to equal -18, but add to equal -3, which are -6 and 3)

(x – 6)(x + 3) = 0

x – 6 = 0 or x + 3 = 0