3a^2-9a-106=-10

Question

how do you factor by complete the square?

Answer 1

3a² - 9a - 106 = -10

 

 

When completing the square, we want one side of the equation to have a term such that we have (a ± c)² , where c is a constant.

 

First, lets add 10 to both sides of the equation.

 

3a² - 9a - 96 = 0

 

 

Next, we can divide both sides of the equation by 3.  Doing this will allow us to have a² term a coefficient of 1.

 

a² - 3a - 32 = 0

 

 

Next, we add 32 on both sides of the equation.

 

a² - 3a = 32

 

 

Finally, we add a number to both sides of the equation that will make the left side a perfect square.

 

Add (-3/2)² on both sides of the equation.

 

a² - 3a + (-3/2)² = 32 + (-3/2)²

 

a² - 3a + (9 / 4) = 32 + (9 / 4)

 

(a - 3/2)(a - 3/2) = (128 / 4) + (9 / 4)

 

(a - 3/2)² = 137 / 4

 

 

Since we are only asked to factor by completing the square, we do not need to anything more to solve for the variable.

Answer 2

3a²-9a-96 =0

a²-3a -32=0

a²-3a + 9/4 -9/4-32=0

(a-3/2)²=32+9/4= 137/4

a-3/2 = ±√137/2

a = 3/2 ±√137/2