Solve by factoring
x^2 -2x -24=0
can you think of 2 numbers, one + the other -, so when multiplied you get -24 and when added you get -2 ?
how about -6,+4 ?
so ...
x^2 -2x -24=0
(x-6)(x+4) = 0
x = 6 or x = -4
To solve the equation x^2 - 2x - 24 = 0 by factoring, we need to find two numbers that multiply to -24 and add up to -2.
Let's list the factor pairs of -24:
-1*24 = -24
-2*12 = -24
-3*8 = -24
-4*6 = -24
Among these factor pairs, the pair that adds up to -2 is -4 and 6.
Now, we can rewrite the original equation as:
(x - 4)(x + 6) = 0
To find the values of x, we set each factor equal to zero and solve for x:
x - 4 = 0 or x + 6 = 0
For x - 4 = 0, add 4 to both sides of the equation:
x = 4
For x + 6 = 0, subtract 6 from both sides of the equation:
x = -6
Therefore, the solutions to the equation x^2 - 2x - 24 = 0 are x = 4 and x = -6.
To solve the given quadratic equation, x^2 - 2x - 24 = 0, we need to factor the equation and find the values of x that make the equation true.
Step 1: Split the middle term
In order to factor the quadratic equation, look for two numbers that multiply to give the product of the coefficient of x^2 (which is 1 in this case) and the constant term (which is -24 in this case), i.e., numbers whose product is -24 and sum is -2.
The numbers -6 and 4 satisfy this condition because (-6) * 4 = -24 and (-6) + 4 = -2.
Step 2: Rewrite the equation
Rewriting the equation with the help of the two numbers, we get:
x^2 - 6x + 4x - 24 = 0
Step 3: Grouping
Group the terms as follows:
(x^2 - 6x) + (4x - 24) = 0
Step 4: Factor by grouping
Factor out the greatest common factor from each group:
x(x - 6) + 4(x - 6) = 0
Step 5: Factor out the common binomial factor
Factor out the common binomial factor, (x - 6), from both terms:
(x - 6)(x + 4) = 0
Step 6: Set each factor equal to zero
Set each factor equal to zero and solve for x:
x - 6 = 0 ---> x = 6
x + 4 = 0 ---> x = -4
Step 7: Final Solution
Therefore, the solutions to the given quadratic equation x^2 - 2x - 24 = 0 are x = 6 and x = -4.