How do you solve $∣ ∣ x^{2} + 2 x - 24 ∣ ∣ = 24$ $|x ^ { 2} + 2x - 24| = 24$ ?

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Answer 1 · 2017-10-22T18:29:00

Let's have a look.

Given,

$∣ ∣ x^{2} + 2 x - 24 ∣ ∣ = 24$ $color(red)(|x^2+2x-24|=24)$

$:.x^2+2x-24=+-24$

Now, the two equations obtained are:

$x^2+2x-24=+24$ ..........(1).

$:.color(red)(x^2+2x-48=0)$

$:.(x+8)(x-6)=0$

So, either $x=6$ or $x=-8$ .

&

$x^2+2x-24=-24$ ..........(2).

$:.color(red)(x^2+2x=0)$

$:.x(x+2)=0$

So, either $x=-2$ or $x=0$ .

Therefore, the four solutions of $x$ are $color(red)(-8,-2,0,6)$ . (Answer).

How do you solve |x ^ { 2} + 2x - 24| = 24∣∣x2+2x−24∣∣=24|x ^ { 2} + 2x - 24| = 24?