+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
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!!.
+129850 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
