solve the equation: x^2 - x - 90 = 0?

Question

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

Answer 1

(x-10)(x+9)=0
x=10
x=-9
what 2 numbers can be multiplied to get -90 and add to get -1

Answer 2

x² - x - 90 = 0

The middle term is - x

Find the sum of the middle term

First term x² = 1

multiply the first term 1 times the last term 90 equals 90 and factor

factors of 90 are

1 x 90
2 x 45
3 x 30
5 x 18
6 x 15
9 x 10. . .←. .use these factors

- 10 and + 9 satisfy the sum of the middle term

insert - 10x and + 9x into the equation

x² - x - 90 = 0

x² - 10x + 9x - 90 = 0

x(x - 10) + 9(x - 10) = 0

(x + 9)(x - 10) = 0

- - - - - - - -

Roots

x + 9 = 0

x + 9 - 9 = 0 - 9

x = - 9

- - - - - - - -

Roots

x - 10 = 0

x - 10 + 10 = 0 + 10

x = 10

- - - - - - - -s-

Answer 3

Hey there!

Here's the answer.

x^2-x-90=0--> Given
x^2-10x+9x-90=0--> Group the terms together
x(x-10)+9(x-10)=0--> Factor out the GCF
(x+9)(x-10)=0--> Gather the factored terms together.
x+9=0, x-10=0--> Use the zero product property.
x=-9, x=10--> Solve the equation for x.
{-9,10} Write the solutions in the set as shown.

The solutions were x=-9 and x=10. I used the grouping method and the zero product property to solve this equation.

Hope it helps!

Answer 4

10

Answer 5

x^2 - x -90 = 0
x^2 - 10x + 9x - 90 = 0
x( x-10) + 9(x-10) =0
(x-10)(x+9)=0
x= 10 , -9

Answer 6

x^2 - x - 90 = 0

(x - 10) (x + 9) = 0

So x = 10 or x = -9 to make the equation valid.

Answer 7

x^2 - 10x + 9x - 90 = 0

therefore (x-10)(x+9) = 0

therefore x = 10 or x = -9

Answer 8

x= -9, 10

Answer 9

First find factors of x²:-
(x-------).(x-----)
Now require factors of 90 that combine with x and x to give - x.
These factors are -10 and 9:-
(x - 10).(x + 9) = 0
x = 10 , x = 9
Check
x.(x + 9) - 10.(x + 9)
x² + 9x - 10x - 90
x² - x - 90 as required

Answer 10

x^2-10x+9x-90=0
x(x-10)+9(x-10)=0
x+9 (x-10)=0
this meanzz x-10=0
therfor x=10
also x-9=0
therfor x=9
answr izz x=10,9