Solve the quadratic function by completing the square. What are the missing pieces in the steps?
–32 = 2(x2 + 10x)
–32 + = 2(x2 + 10x + 25)
18 = 2(x + 5)2
9 = (x + 5)2
± = x + 5
x = –2 or x =

x = - 2 or x = - 8

Step-by-step explanation:

Given

2(x² + 10x) = - 32 ( divide both sides by 2 )

x² + 10x = - 16

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(5)x + 25 = - 16 + 25

(x + 5)² = 9 ( take the square root of both sides )

x + 5 = ± = ± 3 ( subtract 5 from both sides )

x = - 5 ± 3, thus

x = - 5 + 3 = - 2 or x = - 5 - 3 = - 8

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

descending order means to order the polynomials from the term with the largest exponent to the term with the smallest exponent.  

therefore, the correct answer is d.