How do you solve the inequality (x+6)2≤8?

1 Answer
Jim G.
Jun 20, 2018

−6−2√2≤x≤−6+2√2

Explanation:

subtract 8 from both sides

(x+6)2−8≤0

solve (x+6)2−8=0

using difference of squares

∙xa2−b2=(a−b)(a+b)

with a=x+6 and b=√8=2√2

=(x+6−2√2)(x+6+2√2)=0

x+6−2√2=0⇒x=−6+2√2

x+6+2√2=0⇒x=−6−2√2

since coefficient of x2>0 then minimum ⋃

−6−2√2≤x≤−6+2√2
graph{(x+6)^2-8 [-16.02, 16.01, -8.01, 8.01]}

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