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 !

Answer Number 1 :

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

x = 6, -3 <===ANSWER

Moon rose has it right.

You can also use the quadratic equation (when you can’t simplify like she did above) there is no way to write it any simpler. You will get the same answer anyway.

x= { (-b) +- Sqroot [ b(squared) + (4 * a * c) ] } / (2 * a)