Solutions and Solution Sets - College Algebra
Card 1 of 8
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting 
- and, subsequently, 
this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as 
, replacing the two question marks with integers with product 
and sum 5; these integers are 
.
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is 
.
By substituting
We are looking to factor the quadratic expression as
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting 
- and, subsequently, 
this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as 
, replacing the two question marks with integers with product 36 and sum 
; these integers are 
.
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is 
.
By substituting
We are looking to factor the quadratic expression as
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product 36 and sum ; these integers are .
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product and sum 5; these integers are .
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product 36 and sum ; these integers are .
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product and sum 5; these integers are .
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product 36 and sum ; these integers are .
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
These factors can themselves be factored as the difference of squares:
Set each factor to zero and solve:
The solution set is
← Didn't Know|Knew It →
Give all real solutions of the following equation:
Give all real solutions of the following equation:
Tap to reveal answer
By substituting - and, subsequently, this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product and sum 5; these integers are .
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is .
By substituting
We are looking to factor the quadratic expression as
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is
← Didn't Know|Knew It →