Problem 1085

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then, write and factor the trinomial.

x2 – 14x

 

Solution : –

 

If  x2 + bx is a binomial, then by adding (\frac{b}{a})^{2} , which is the square of half the coefficient of x, a perfect square trinomial will result.

x + bx +(\frac{b}{a})^{2} = (x+\frac{b}{a})^{2}

To complete the square, add the square of half the coefficient of x.

The coefficient of x is -14, so half the coefficient is –\frac{14}{2} = -7.

The square of half the coefficient of x, -7x is (-7)2 = 49.

To write the trinomial, add the constant 49 to the original expression. The resulting  perfect .

To write the trinomial, add the constant 49 to the original expression. The resulting perfect square trinomial is x2 – 14x + 49.

Finally, factor the trinomial x2 – 14x + 49.

x2 -14x + 49  =  (x – 7)2

 

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