Question

Make x the subject of the formula y = x^2

Answer 1

Answer:

$\displaystyle \large{x=\pm \sqrt{y}}$

Step-by-step explanation:

We are given the equation:

$\displaystyle \large{y=x^2}$

Make ‘x’ the subject of the formula by square root both sides:

$\displaystyle \large{\sqrt{y}=\sqrt{x^2}}$

Cancel the square root and square in RHS and write plus-minus in LHS:

$\displaystyle \large{\pm \sqrt{y}= x}\\\displaystyle \large{x=\pm \sqrt{y}}$

Therefore, the solution is $\displaystyle \large{x=\pm \sqrt{y}}$

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Summary

To make a variable as the subject of equation means to isolate that variable. For an example, if you want to make y as the subject, you’ll have to isolate y-term.

You may also be curious why do you have to add plus-minus on another side when cancelling $\displaystyle \large{\sqrt{x^2}}$ because $\displaystyle \large{\sqrt{x^2}=|x|}$ and $\displaystyle \large{|x|}$ for their positive and their counterparts (opposite/negative) will always give same y-value.

From an example:

$\displaystyle \large{\sqrt{x^2}=4}$ can be rewritten as $\displaystyle \large{|x|=4}$, cancel absolute sign/square root then write plus-minus which the solution is $\displaystyle \large{x=\pm 4}$ and if you substitute x = 4 or -4, the equation will be true for both values.

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Others

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