Question

Work out the value of a in the equation below.
x^2 - 14x+49= (x − a)^2

Answer 1

`a=7`

Explanation:

we can expand the right hand side:

`(x-a)^2=(x-a)(x-a)=x^2-ax-ax+a^2=x^2-2ax+a^2`

now, compare with the left hand side:

`x^2-14x+49=x^2-2ax+a^2`

we have two equations relating a:

`a^2=49\\2a=14`

solving either one would yield:
`2a=14\implies a=7.` this solution is correct for both equations.

Answer 2

`a = 7`

Explanation:

Let's expand the right side of the equation
`(x - a)^2` and then set it equal to
`x^2 - 14x + 49`.

`(x - a)^2 = x^2 - 2ax + a^2`

Now, set it equal to
`x^2 - 14x + 49`:

`x^2 - 2ax + a^2 = x^2 - 14x + 49`

Now, compare the coefficients of corresponding terms:

1. Coefficient of
`x^2`:
`1 = 1` (no change)

2. Coefficient of
`x`:
`-2a = -14`

Now, solve for
`a`:

`-2a = -14`

Divide both sides by -2:

`\sf (-2a)/(-2)=(-14)/(-2)`

`a = 7`

So, the value of
`a` in the equation
`x^2 - 14x + 49 = (x - a)^2` is
`a = 7`.