MHB Why Are There No Real Solutions to the Equation \( |x^2 + 4x| = -12 \)?

[mathdad]

Explain why there are no real numbers that satisfy the equation
$$|x^2 + 4x| = - 12$$
How is this done algebraically?

 

[skeeter]

Explain why there are no real numbers that satisfy the equation

|x^2 + 4x| = - 12

because ...

$|\text{whatever}| \ge 0$

How is this done algebraically?

solve each case ...

case 1 ... $x^2+4x \ge 0 \implies x^2+4x+12 = 0$ ... recommend looking at the discriminant

case 2 ... $x^2+4x < 0 \implies -x^2-4x+12 = 0$ ... check the two real solutions in the original abs equation.

 

[mathdad]

See attachment for my little outline.

View attachment 7492

 

[skeeter]

$|whatever| \ge 0 \implies |whatever| \nless 0$

... that's it.

 

[mathdad]

Great. We now move on to the next topic.