How do you solve (x+2)2=−7?

2 Answers
ste b.
Mar 25, 2018

No solution

Explanation:

(x+2)2=−7
x2+4x+4=−7
x2+4x+11=0

Now I use the discriminant to determine if there is a solution

b2−4ac

42−(4.7)
16−28

Already, discriminant is less than zero there there are no real solutions for x.

Jensen Z
Mar 25, 2018

x=−2±i√7

Explanation:

There are many ways to tackle this; the easiest and quickest way here would be the square root method: take the square root of both sides:

√(x+2)2=±√−7

x+2=±√−7

Since you cannot take the square root of a negative and get a real number, there is no real solution to this equation. However, we can simplify to get a complex solution:

x+2=±√7⋅√−1

x+2=±i√7

x=−2±i√7

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