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X 2 −51=14xx, squared, minus, 51, equals, 14, x 1) Rewrite the equation by completing the square.

User Jeff Jirsa
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1 Answer

6 votes

Answer:

(x -7)² = 100

Explanation:

You want to rewrite the equation x² -51 = 14x by completing the square.

Complete square

When we're finished, the equation will be of the form ...

(x +a)² = b

Expanding this, we have ...

x² +2ax +a² = b

That is, the value of 'a' is half the coefficient of x when the equation is written with the x-terms together.

Rearrangement

Adding 51 -14x to both sides of the given equation, we get ...

x² -51 = 14x

x² -14x = 51

Now, we can see that a=-14/2 = -7. We can add a² = (-7)² = 49 to both sides to complete the square:

x² -14x +49 = 51 +49

(x -7)² = 100 . . . . . . . rewritten equation

User Natz
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