solve the equation: x^2 - 15x - 54 = 0.?

Question

Solve this question correct with detailed workings and earn points!!! :)

Answer 1

Hi,

In x² - 15x - 54, there is no GCF to factor out.

Then to make your 2 binomials, x² would split into x and x in both parentheses.

(x...)(x...)

The first parentheses gets the first sign from in front of the x term.

(x.-..)(x...)

The second parentheses gets the sign you would get from multiplying the 2 signs in the problem together. Since they are both negative, a negative times a negative gives a positive answer. therefore put a + in the second parentheses.

(x.-..)(x.+..)

Multiply the "a" and "c" values together from the first and third
terms. (Ignore their signs - you've already done your signs.)
1 x 54 = 54, so list pairs of factors of 54.

54
------
1*54
2*27
3*18
6*9

If the signs you put in the parentheses are the SAME, then find factors that ADD to 15, your value of "b".
If the signs you put in the parentheses are DIFFERENT, then find factors that SUBTRACT to 15, your value of "b".

You want factors that subtract to 15, so use 3 and 18.

The BIGGER number is always pushy, so it goes first in the parentheses. You get:

(x - 18)(x + 3) = 0

Now set each factor with a variable equal to zero and solve.

If x - 18 = 0, then x = 18

If x + 3 = 0 then x = -3


I hope that helps!! :-)

Answer 2

Hey there!

Here's the answer!

x^2-15x-54=0 --> Given
x^2-18x+3x-54=0 --> Group the terms together
x(x-18)+3(x-18)=0 --> Factor out the GCF
(x+3)(x-18)=0 --> Gather the terms together.
x+3=0, x-18=0 --> Apply the zero product property
x=-3, x=18 --> Solve the equation for x
{-3.18} The solutions can be written in a set as shown

I used the grouping method and the zero product property in solving this equation.

Thus the solution is x=-3 or x=18.

I hope it helps!

Answer 3

x² - 15x - 54 = 0

The middle term is - 15x

Find the sum of the middle term

First term x² = 1

Multiply the first term 1 times the last term 54 equals 54 and factor

Factors of 54

1 x 54
2 x 27
6 x 9. . .←. . use these factors

- 9 and - 6 satisfy the sum of the middle term

insert - 9x and - 6x into the equation

x² - 15x - 54 = 0

x² - 9x - 6x - 54 = 0

x(x - 9) - 6(x - 9) = 0

(x - 6)(x - 9) = 0

- - - - - - - -

Roots

x - 6 = 0

x - 6 + 6 = 0 + 6

x = 6

- - - - - - -

Roots

x - 9 = 0

x = 9 + 9 = 0 + 9

x = 9

- - - - - - - -s-

Answer 4

Require factors of x² and these are x and x as follows:-
(x-------).(x------)
Now require factors of -54 that combine with x and x to give - 15x.
These are -18 and 3 :-
(x - 18).(x + 3) = 0
x = 18 , x = - 3
Check
x.(x + 3) - 18.(x + 3)
= x² + 3x - 18x - 54
= x² - 15x - 54 as required

Answer 5

Factor this:x^2-15x-54+=0
These are your factors:(x-8)(x-7)=0
Set each factor equal to zero:x-8=0 x-7=0
There's your answer: x=8 and x=7

Answer 6

(x-18)(x+3)=0
what 2 numbers can be multiplied to get -54 but also can be added to get -15
x=18
x=-3

Answer 7

The easiest way to solve tis would be to type it into a graphing calculator. It's a good investment, I'd say. Kind of expensive, but totally worth it. It saves you so much time. Good luck. :)