Question

solve for x:x^2 + 24 =0​

Answer 1

Answer:

$x^{2} +24\\x^{2} =-24$

Square root both sides,

$\sqrt{ x^{2} }=\sqrt{24}$

$x=\sqrt{2*2*2*3}$

$x=2\sqrt{6}$

Answer 2

x = 2√6 i, -2√6 i

Step-by-step explanation:

The given equation is

$x^2+24=0$

or, $x^2+0x+24=0$

Comparing it with general quadratic equation $ax^2+bx+c=0]$

We get

$a=1$

$b=0$

$c=24$

Using the quadratic formula

We know that solution of general quadratic equation  $ax^2+bx+c=0]$ is given by

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Therefore, the solution will be

$x=\frac{-0\pm\sqrt{0^2-4\times 1\times 24}}{2\times 1}$

$\implies x=\frac{\pm\sqrt{-4\times 4\times 6}}{2}$

$\implies x=\frac{\pm4\sqrt{-6}}{2}$

$\implies x=\pm2\sqrt{-6}$

$\implies x=\pm2\sqrt{6}i$         where $i=\sqrt{-1}$

Hope this answer is helpful.

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