Question

What are the solutions to the equation?

a^2 −10a + 25 = 49

Enter your answers in the boxes.

a1 =

a2 =

Answer 1

Subtract 49 from both sides to get equation into
`a x^(2) +bx+c=0` form:


`a^(2) -10a-24=0`

Then factor:


`(a-12)(a+2)=0`

Solutions corresponding to these factors are
`a=12` and
`a=-2`.

Answer 2

`a_(1)= 12` and
`a_(2)= -2`.

Explanation:

We are given the equation,

`a^2-10a+25=49`

i.e.
`a^2-10a=49-25`

i.e.
`a^2-10a=24`

i.e.
`a^2-10a-24=0`

i.e.
`(a-12)(a+2)=0`

i.e.
`(a-12)=0` and
`(a+2)=0`

i.e. a= 12 and a= -2

Hence, the solutions of the given equation are,

`a_(1)= 12` and
`a_(2)= -2`.