2. What is a solution of x² + 6x = –5?

x = –6

x = –1

x = 1

x = 6

3. Which of the following is a solution of x² + 14x + 112 = 0? If necessary, round to the nearest hundredth.

x = –0.24

x = –4.24

4.24

no solution

ribbondollop45
Mar 21, 2017

#1**0 **

Solve for x

x^2 + 6 x = -5

Add 9 to both sides:

x^2 + 6 x + 9 = 4

Write the left hand side as a square:

(x + 3)^2 = 4

Take the square root of both sides:

x + 3 = 2 or x + 3 = -2

Subtract 3 from both sides:

x = -1 or x + 3 = -2

Subtract 3 from both sides:

**Answer: | x = -1 or x = -5**

Solve for x:

x^2 + 14 x + 112 = 0

Subtract 112 from both sides:

x^2 + 14 x = -112

Add 49 to both sides:

x^2 + 14 x + 49 = -63

Write the left hand side as a square:

(x + 7)^2 = -63

Take the square root of both sides:

x + 7 = 3 i sqrt(7) or x + 7 = -3 i sqrt(7)

Subtract 7 from both sides:

x = 3 i sqrt(7) - 7 or x + 7 = -3 i sqrt(7)

Subtract 7 from both sides:

**Answer: | x = 3 i sqrt(7) - 7 or x = -3 i sqrt(7) - 7**

**P.S. Neither solution agrees with your multiple choices!!.**

Guest Mar 21, 2017

#2**+2 **

2. x^2 + 6x = -5 add 5 to both sides

x^2 + 6x + 5 = 0 factor

(x + 5) ( x + 1) = 0 set each factor to 0

x + 5 = 0 x + 1 = 0

x = -5 x = -1 and these are the solutions

3. x^2 + 14x + 112 = 0

Using the discriminant we have

14^2 - 4(1)(112) =

196 - 448 =

-252 ....so this has no real solution

CPhill
Mar 21, 2017