solve this equation by factoring
a^2-8a=-15 the a^2 is a' squared
you can add 15 to both sides and then factor a^2-8+15=0
you have to find 2 numbers that when added together equal -8 and when multiplied equals 15...-5 and -3
after factoring you should get
a-5=0 & a-3=0
then a=5 and a=3
First add 15 to both sides to get all terms on one side of the equal side and a zero on the other:
a^2-8a+15=0 Then set up your parentheses.
( )( )=0 Now ask yourself, what two things multiplied together = a^2? a*a So put one of each in the first place in the parentheses.
(a )(a )=0 Now look for two #s that multiply to get 15 and add or subtract to get 8. That would be 3 and 5. Put one of each of those in the second place in the parentheses.
(a 3)(a 5)=0 Now you have to decide what signs they get. Since they have to equal -8a when you add them together, the only way that can happen if they're both negative. Only -3+-5 can give you -8.
(a-3)(a-5)=0 Now set each factor equal to zero and solve each separately.
a-3=0 and a-5=0
a=3 and a=5
Remember that this type of factoring is the opposite of FOILing, which you must have learned already. So you can always FOIL it back to see if your answer is correct.
To solve the equation by factoring, we need to rewrite the equation in the form of a quadratic equation where one side is equal to zero.
Given equation: a^2 - 8a = -15
To rewrite the equation, we move all the terms to one side to have zero on the other side:
a^2 - 8a + 15 = 0
Now, we need to factorize the quadratic expression a^2 - 8a + 15.
We need to find two numbers that, when multiplied, give 15, and when added, give -8. In this case, the two numbers are -3 and -5.
So, we can rewrite the equation as:
(a - 3)(a - 5) = 0
Now, we set each factor equal to zero and solve for 'a':
a - 3 = 0 or a - 5 = 0
Solving the first equation:
a - 3 = 0
Adding 3 to both sides:
a = 3
Solving the second equation:
a - 5 = 0
Adding 5 to both sides:
a = 5
Therefore, the solutions to the quadratic equation are a = 3 and a = 5.