Question

Which of the following are solutions to the equation below?

Check all that apply.

4x^2 + 20x + 25 = 49

A. x = -1

B. x = 1

C. x = 6

D. x = -6

E. x = √7-5/2

F. x = -√7-5/2

Answer 1

`\qquad\qquad\huge\underline{{\sf Answer}}`

Let's solve the given equation ~

`\qquad \tt \dashrightarrow \:4 {x}^(2) + 20x + 25 = 49`

`\qquad \tt \dashrightarrow \:4 {x}^(2) + 20x + 25 - 49 = 0`

`\qquad \tt \dashrightarrow \:4 {x}^(2) + 20x - 24 = 0`

`\qquad \tt \dashrightarrow \:4( {x}^(2) + 5x - 6) = 0`

`\qquad \tt \dashrightarrow \: {x}^(2) + 5x - 6 = 0`

`\qquad \tt \dashrightarrow \: {x}^(2) + 6x - x - 6 = 0`

`\qquad \tt \dashrightarrow \:x(x + 6) - 1(x + 6) = 0`

`\qquad \tt \dashrightarrow \:(x + 6)(x - 1) = 0`

Hence, we get -6 and 1 as our roots ~

So, the correct choices are : B and D