Question

Help needed : TexFormula1" title=" \quad \sf \: {x}^{2} = 1 - 37" alt=" \quad \sf \: {x}^{2} = 1 - 37" align="absmiddle" class="latex-formula">

solve for x ​

Answer 1

Answer:

• x = 6i, -6i

Step-by-step explanation:

$\sf x^2=1-37$

Subtract 37 from 1 = -36

$\boxed{\sf x^2=? :\: x=\sqrt{?},\:\:-\sqrt{?}}$

$\sf x=\sqrt{-36}$

$\sf x=-\sqrt{-36}$

Apply Radical Rule:-

$\boxed{ \sf \sqrt{-a}=\sqrt{-1}\sqrt{a}}$

$\sf \sqrt{-36}=\sqrt{-1}\sqrt{36}$

$\sf \sqrt{-1}\sqrt{36}$

$\boxed{\sf \sqrt{-1 }=i}$

$\sf \sqrt{36}i$

$\sf 6i$

___________

$\sf x=-\sqrt{-36}$

$\sf -\sqrt{-36}$

$\sf -6i$

Therefore, x = 6i, -6i.

__________________________

Answer 2

Answer:

x = 6i, -6i

Explanation:

x² = 1 - 37                 (subtract)

x² = -36                   (square root both sides)

x = ±√-36                 (breakdown)

x = +√-36, -√-36      (simplify)

x = 6i, -6i