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

Work out the value of a in the equation below. x^2 - 14x+49= (x − a)^2-example-1
User JenEriC
by
8.1k points

2 Answers

2 votes

Answer:


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.

User Atimb
by
7.8k points
5 votes

Answer:


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.

User HazemGomaa
by
8.4k points

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