Question

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

Answer 1

`\displaystyle \large{x=\pm √(y)}`

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{√(y)=√(x^2)}`

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

`\displaystyle \large{\pm √(y)= x}\\\displaystyle \large{x=\pm √(y)}`

Therefore, the solution is
`\displaystyle \large{x=\pm √(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{√(x^2)}` because
`\displaystyle \large√(x^2)=` and
`\displaystyle \large` for their positive and their counterparts (opposite/negative) will always give same y-value.

From an example:

`\displaystyle \large{√(x^2)=4}` can be rewritten as
`\displaystyle \largex`, 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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