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# Math

+1
133
2
+9

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
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### 2+0 Answers

#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
+79894
+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

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