Number of Solutions
Solve by Graphing
Factoryng
Solving by Factoring
Mystery...
Or is it?
Or is it?
101
The number of solutions for the equation
x^2=81
2 Solutions
x=9
x=-9
101
The number of solutions to the equation
x^2+5x+9=0
No Solution.
The graph doesn't have an x-intercept.
101
Rewrite the expression in factored form. If it cannot be done, write "cannot be done".
x^2-400
(x+20)(x-20)
101
Solve by factoring.
4x^2=16x
x=0 and x=4
4x^2-16x=0
4x(x-4)
101
Solfe the equation.
(x-4)(2x+6)=0
x=4 and x=-3
200
The number of solutions for the equation
9x^2=0
1 Solution
x=0
200
The number of solutions to the equation
x^2-5x-36=0
3 Solutions.
The graph has x-intercepts at -4 and 9.
200
Rewrite the expression in factored form. If it cannot be done, write "cannot be done".
x^2+16
Cannot be done.
200
Solve by factoring.
x^2-x-6=0
x=3 and x=-2
(x-3)(x+2)=0
200
Kiran is solving the equation given below. His first step was to divide both sides by 4x. He says the only solution is x=0.5. Explain to Kiran why dividing by 4x is not a good first step and find both solutions to the equation.
8x^2=4x
Dividing by 4x is not valid when x=0, because it would mean dividing by 0.
Instead, Kiran should subtract 4x from both sides. Then he can factor the equation as shown below and get solutions of x=0 and x=0.5.
8x^2-4x=0
4x(2x-1)=0
300
The number of solutions to the equation
x^2=-25
No Solutions.
A number squared cannot equal a negative number.
300
The number of solutions to the equation
x^2-4x+4=0
1 Solution.
The graph has one x-intercept at 2.
300
Rewrite the expression in factored form. If it cannot be done, write "cannot be done".
25x^2-9/16
(5x+3/4)(5x-3/4)
300
Solve by factoring.
x^2+9x+20=0
x=-4 and x=-5
(x+4)(x+5)=0
300
Choose the expressions that are equivalent to
x^2+4x+3
A. (x+2)^2-1
B. (x+2)^2+1
C. (x-1)(x-3)
D. (x+1)(x+3)
E. (x-1)(x+4)
A and D
400
The number of solutions to the equation is 2.
x^2-5=31
I already told you the answer why are you here?
x=6
x=-6
400
Here is a graph. Lin says that the equation
-x^2-4=0
has 1 solution because the y-intercept is at -4. Determine if Lin is correct.
Lin is incorrect. This equation has no solutions because it doesn't have an x-intercept. Lin accidentally looked at the y-intercept instead of the x-intercept.
400
Rewrite the expression in factored form. If it cannot be done, write "cannot be done".
x^2+2x-24
(x-4)(x+6)
400
Solve by factoring.
x^2-1600=0
x=40 or x=-40
(x-40)(x+40)=0
400
The two expressions below are equivalent. Find the values of a and b that make the expressions equivalent.
5x^2+bx-12
(5x+a)(x-4)
a=3 and b=-17
500
The number of solutions to the equation is 2.
(x+4)(x-4)=0
I already said the answer... Why are you here?
x=-4
x=4
500
How can the graph tell us how many solutions there are?
The number of x-intercepts reveals the number of solutions.
500
Rewrite the expression in factored form. If it cannot be done, write "cannot be done".
t^2-5t+6
You're mistaken...
500
Solve by factoring.
x^2-2x-24=0
x=-4 and x=6
(x+4)(x-6)=0
500
A fenced-in community garden currently has a square plot of land with a side length of x. They decide to change the shape of the garden to a rectangle while still using the same amount of fencing materials. The equation below represents the relationship of the new side lengths with the garden's area. Find the original side length of the garden.
(x+5)(x-5)=299
x=18 (a negative value for x wouldn't make sense)
x^2-25=299
x^2=324
x=18 or x=-18