Question

How do I do this lol

Answer 1

x = 6, x = 7

Explanation:

Given

x =
`√(13x-42)` ← square both sides

x² = 13x - 42 ← subtract 13x - 42 from both sides

x² - 13x + 42 = 0 ← in standard form

(x - 6)(x - 7) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x - 7 = 0 ⇒ x = 7

As a check substitute these values into the right side of the equation and if equal to the left side then they are the solutions

x = 6 :
`√(78-42)` =
`√(36)` = 6 ← solution

x = 7 :
`√(91-42)` =
`√(49)` = 7 ← solution

Answer 2

Assignment:
`\bold{Solve \ Equation: \ x=√(13x-42)}`

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Answer:
`\boxed{\bold{x=7,\:x=6}}`

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Explanation:
`\downarrow\downarrow\downarrow`

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[ Step One ] Square Both Sides

`\bold{x^2=\left(√(13x-42)\right)^2}`

[ Step Two ] Expand
`\bold{\left(√(13x-42)\right)^2}`

`\bold{13x-42}`

[ Step Three ] Rewrite Equation

`\bold{x^2=13x-42}`

[ Step Four ] Solve
`\bold{x^2=13x-42}`

`\bold{x=7,\:x=6}`

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`\bold{\rightarrow Mordancy \leftarrow}`