To solve the given equation by factoring, we will start by writing all the terms on the left-hand side. Then, we will factor out the GCF. Afterwards, we will apply the Zero Product Property to solve the equation.
Since the GCF is 1, we did not need to factor anything out in this situation. To find the solutions, we will solve the equation. Note that this is a quadratic equation. Thus, we will use the Quadratic Formula.
ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2a
To do so, we first need to identify a, b, and c.
x^2-11x+24=0 ⇔ 1x^2+( - 11)x+ 24=0
We see that a= 1, b= - 11, and c= 24. Let's substitute these values into the formula and solve for x.
The solutions for this equation are x= 11± 52. Let's separate them into the positive and negative cases.
x=11± 5/2
x_1=11+5/2
x_2=11-5/2
x_1=16/2
x_2=6/2
x_1=8
x_2=3
Using the Quadratic Formula, we found that the solutions of the given equation are x_1=8 and x_2=3.
These solutions to the quadratic equation are also solutions for the given equation.
