Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then
write and factor the trinomial.
-$$x ^ { 2 } + 8 x = 7$$
A) $\{ - 4 - \sqrt { 11.5 } , - 4 + \sqrt { 11.5 } \}$
B) $\{ 4 + \sqrt { 11.5 } \}$
C) $\{ - 1 - \sqrt { 11.5 } , - 1 + \sqrt { 11.5 } \}$
D) $\{ - 4 - 1 \sqrt { 11.5 } , - 4 + 1 \sqrt { 11.5 } \}$

Question

Quizplus · Accepted Answer

To make the binomial a perfect square trinomial, we need to add the square of half the coefficient of the x-term. In this case, the coefficient of the x-term is 8, so half of that is 4. The square of 4 is 16, so we need to add 16 to the binomial. This gives us:$$x^2 + 8x + 16 = 7 + 16 = 23$$Now we can factor the trinomial as:$$(x + 4)^2 = 23$$

Determine the Constant That Should Be Added to the Binomial x2+8x=7x ^ { 2 } + 8 x = 7x2+8x=7

Determine the Constant That Should Be Added to the Binomial $x ^ { 2 } + 8 x = 7$